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An Invitation to Statistics in Wasserstein Space / Victor M. Panaretos / Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer (2020)
Titre : An Invitation to Statistics in Wasserstein Space Type de document : document électronique Auteurs : Victor M. Panaretos, ; Yoav Zemel, ; SpringerLink (Online service) Editeur : Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer Année de publication : 2020 Collection : SpringerBriefs in Probability and Mathematical Statistics, ISSN 2365-4333 Importance : XIII, 147 p. 30 illus., 24 illus. in color Présentation : online resource ISBN/ISSN/EAN : 978-3-030-38438-8 Langues : Anglais (eng) Tags : Probabilities Probability Theory and Stochastic Processes Résumé : This open access book presents the key aspects of statistics in Wasserstein spaces, i.e. statistics in the space of probability measures when endowed with the geometry of optimal transportation. Further to reviewing state-of-the-art aspects, it also provides an accessible introduction to the fundamentals of this current topic, as well as an overview that will serve as an invitation and catalyst for further research. Statistics in Wasserstein spaces represents an emerging topic in mathematical statistics, situated at the interface between functional data analysis (where the data are functions, thus lying in infinite dimensional Hilbert space) and non-Euclidean statistics (where the data satisfy nonlinear constraints, thus lying on non-Euclidean manifolds). The Wasserstein space provides the natural mathematical formalism to describe data collections that are best modeled as random measures on Euclidean space (e.g. images and point processes). Such random measures carry the infinite dimensional traits of functional data, but are intrinsically nonlinear due to positivity and integrability restrictions. Indeed, their dominating statistical variation arises through random deformations of an underlying template, a theme that is pursued in depth in this monograph Note de contenu : Optimal transportation -- The Wasserstein space -- Fréchet means in the Wasserstein space -- Phase variation and Fréchet means -- Construction of Fréchet means and multicouplings Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=149822 An Invitation to Statistics in Wasserstein Space [document électronique] / Victor M. Panaretos, ; Yoav Zemel, ; SpringerLink (Online service) . - Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer, 2020 . - XIII, 147 p. 30 illus., 24 illus. in color : online resource. - (SpringerBriefs in Probability and Mathematical Statistics, ISSN 2365-4333) .
ISBN : 978-3-030-38438-8
Langues : Anglais (eng)
Tags : Probabilities Probability Theory and Stochastic Processes Résumé : This open access book presents the key aspects of statistics in Wasserstein spaces, i.e. statistics in the space of probability measures when endowed with the geometry of optimal transportation. Further to reviewing state-of-the-art aspects, it also provides an accessible introduction to the fundamentals of this current topic, as well as an overview that will serve as an invitation and catalyst for further research. Statistics in Wasserstein spaces represents an emerging topic in mathematical statistics, situated at the interface between functional data analysis (where the data are functions, thus lying in infinite dimensional Hilbert space) and non-Euclidean statistics (where the data satisfy nonlinear constraints, thus lying on non-Euclidean manifolds). The Wasserstein space provides the natural mathematical formalism to describe data collections that are best modeled as random measures on Euclidean space (e.g. images and point processes). Such random measures carry the infinite dimensional traits of functional data, but are intrinsically nonlinear due to positivity and integrability restrictions. Indeed, their dominating statistical variation arises through random deformations of an underlying template, a theme that is pursued in depth in this monograph Note de contenu : Optimal transportation -- The Wasserstein space -- Fréchet means in the Wasserstein space -- Phase variation and Fréchet means -- Construction of Fréchet means and multicouplings Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=149822 Analytic Theory of Itô-Stochastic Differential Equations with Non-smooth Coefficients / Haesung Lee / Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer (2022)
Titre : Analytic Theory of Itô-Stochastic Differential Equations with Non-smooth Coefficients Type de document : document électronique Auteurs : Haesung Lee, ; Wilhelm Stannat, ; SpringerLink (Online service) ; Gerald Trutnau, Editeur : Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer Année de publication : 2022 Collection : SpringerBriefs in Probability and Mathematical Statistics, ISSN 2365-4333 Importance : XV, 126 p. 1 illus Présentation : online resource ISBN/ISSN/EAN : 978-981-19383-1-3 Langues : Anglais (eng) Tags : Probabilities Mathematical analysis Functions of real variables Functional analysis Probability Theory Analysis Real Functions Functional Analysis Résumé : This book provides analytic tools to describe local and global behavior of solutions to Itô-stochastic differential equations with non-degenerate Sobolev diffusion coefficients and locally integrable drift. Regularity theory of partial differential equations is applied to construct such solutions and to obtain strong Feller properties, irreducibility, Krylov-type estimates, moment inequalities, various types of non-explosion criteria, and long time behavior, e.g., transience, recurrence, and convergence to stationarity. The approach is based on the realization of the transition semigroup associated with the solution of a stochastic differential equation as a strongly continuous semigroup in the Lp-space with respect to a weight that plays the role of a sub-stationary or stationary density. This way we obtain in particular a rigorous functional analytic description of the generator of the solution of a stochastic differential equation and its full domain. The existence of such a weight is shown under broad assumptions on the coefficients. A remarkable fact is that although the weight may not be unique, many important results are independent of it. Given such a weight and semigroup, one can construct and further analyze in detail a weak solution to the stochastic differential equation combining variational techniques, regularity theory for partial differential equations, potential, and generalized Dirichlet form theory. Under classical-like or various other criteria for non-explosion we obtain as one of our main applications the existence of a pathwise unique and strong solution with an infinite lifetime. These results substantially supplement the classical case of locally Lipschitz or monotone coefficients. We further treat other types of uniqueness and non-uniqueness questions, such as uniqueness and non-uniqueness of the mentioned weights and uniqueness in law, in a certain sense, of the solution Note de contenu : Chapter 1. Introduction -- Chapter 2. The abstract Cauchy problem in Lr-spaces with weights -- Chapter 3.Stochastic differential equations -- Chapter 4. Conclusion and outlook Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=172030 Analytic Theory of Itô-Stochastic Differential Equations with Non-smooth Coefficients [document électronique] / Haesung Lee, ; Wilhelm Stannat, ; SpringerLink (Online service) ; Gerald Trutnau, . - Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer, 2022 . - XV, 126 p. 1 illus : online resource. - (SpringerBriefs in Probability and Mathematical Statistics, ISSN 2365-4333) .
ISBN : 978-981-19383-1-3
Langues : Anglais (eng)
Tags : Probabilities Mathematical analysis Functions of real variables Functional analysis Probability Theory Analysis Real Functions Functional Analysis Résumé : This book provides analytic tools to describe local and global behavior of solutions to Itô-stochastic differential equations with non-degenerate Sobolev diffusion coefficients and locally integrable drift. Regularity theory of partial differential equations is applied to construct such solutions and to obtain strong Feller properties, irreducibility, Krylov-type estimates, moment inequalities, various types of non-explosion criteria, and long time behavior, e.g., transience, recurrence, and convergence to stationarity. The approach is based on the realization of the transition semigroup associated with the solution of a stochastic differential equation as a strongly continuous semigroup in the Lp-space with respect to a weight that plays the role of a sub-stationary or stationary density. This way we obtain in particular a rigorous functional analytic description of the generator of the solution of a stochastic differential equation and its full domain. The existence of such a weight is shown under broad assumptions on the coefficients. A remarkable fact is that although the weight may not be unique, many important results are independent of it. Given such a weight and semigroup, one can construct and further analyze in detail a weak solution to the stochastic differential equation combining variational techniques, regularity theory for partial differential equations, potential, and generalized Dirichlet form theory. Under classical-like or various other criteria for non-explosion we obtain as one of our main applications the existence of a pathwise unique and strong solution with an infinite lifetime. These results substantially supplement the classical case of locally Lipschitz or monotone coefficients. We further treat other types of uniqueness and non-uniqueness questions, such as uniqueness and non-uniqueness of the mentioned weights and uniqueness in law, in a certain sense, of the solution Note de contenu : Chapter 1. Introduction -- Chapter 2. The abstract Cauchy problem in Lr-spaces with weights -- Chapter 3.Stochastic differential equations -- Chapter 4. Conclusion and outlook Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=172030 Asymptotic Properties of Permanental Sequences / Michael B. Marcus / Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer (2021)
Titre : Asymptotic Properties of Permanental Sequences : Related to Birth and Death Processes and Autoregressive Gaussian Sequences Type de document : document électronique Auteurs : Michael B. Marcus, ; Jay Rosen (1956-....), ; SpringerLink (Online service) Editeur : Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer Année de publication : 2021 Collection : SpringerBriefs in Probability and Mathematical Statistics, ISSN 2365-4333 Importance : XI, 114 p. 2 illus., 1 illus. in color Présentation : online resource ISBN/ISSN/EAN : 978-3-030-69485-2 Langues : Anglais (eng) Tags : Probabilities Probability Theory and Stochastic Processes Résumé : This SpringerBriefs employs a novel approach to obtain the precise asymptotic behavior at infinity of a large class of permanental sequences related to birth and death processes and autoregressive Gaussian sequences using techniques from the theory of Gaussian processes and Markov chains. The authors study alpha-permanental processes that are positive infinitely divisible processes determined by the potential density of a transient Markov process. When the Markov process is symmetric, a 1/2-permanental process is the square of a Gaussian process. Permanental processes are related by the Dynkin isomorphism theorem to the total accumulated local time of the Markov process when the potential density is symmetric, and by a generalization of the Dynkin theorem by Eisenbaum and Kaspi without requiring symmetry. Permanental processes are also related to chi square processes and loop soups. The book appeals to researchers and advanced graduate students interested in stochastic processes, infinitely divisible processes and Markov chains Note de contenu : 1.Introduction, General Results and Applications -- 2.Birth and death processes -- 3.Birth and death processes with emigration -- 4.Birth and death processes with emigration related to first order Gaussian autoregressive sequences -- 5.Markov chains with potentials that are the covariances of higher order Gaussian autoregressive sequences -- 6.Relating permanental sequences to Gaussian sequences -- 7. Permanental sequences with kernels that have uniformly bounded row sums -- 8.Uniform Markov chains -- References -- Index. Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=165037 Asymptotic Properties of Permanental Sequences : Related to Birth and Death Processes and Autoregressive Gaussian Sequences [document électronique] / Michael B. Marcus, ; Jay Rosen (1956-....), ; SpringerLink (Online service) . - Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer, 2021 . - XI, 114 p. 2 illus., 1 illus. in color : online resource. - (SpringerBriefs in Probability and Mathematical Statistics, ISSN 2365-4333) .
ISBN : 978-3-030-69485-2
Langues : Anglais (eng)
Tags : Probabilities Probability Theory and Stochastic Processes Résumé : This SpringerBriefs employs a novel approach to obtain the precise asymptotic behavior at infinity of a large class of permanental sequences related to birth and death processes and autoregressive Gaussian sequences using techniques from the theory of Gaussian processes and Markov chains. The authors study alpha-permanental processes that are positive infinitely divisible processes determined by the potential density of a transient Markov process. When the Markov process is symmetric, a 1/2-permanental process is the square of a Gaussian process. Permanental processes are related by the Dynkin isomorphism theorem to the total accumulated local time of the Markov process when the potential density is symmetric, and by a generalization of the Dynkin theorem by Eisenbaum and Kaspi without requiring symmetry. Permanental processes are also related to chi square processes and loop soups. The book appeals to researchers and advanced graduate students interested in stochastic processes, infinitely divisible processes and Markov chains Note de contenu : 1.Introduction, General Results and Applications -- 2.Birth and death processes -- 3.Birth and death processes with emigration -- 4.Birth and death processes with emigration related to first order Gaussian autoregressive sequences -- 5.Markov chains with potentials that are the covariances of higher order Gaussian autoregressive sequences -- 6.Relating permanental sequences to Gaussian sequences -- 7. Permanental sequences with kernels that have uniformly bounded row sums -- 8.Uniform Markov chains -- References -- Index. Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=165037 Concentration of Maxima and Fundamental Limits in High-Dimensional Testing and Inference / Zheng Gao / Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer (2021)
Titre : Concentration of Maxima and Fundamental Limits in High-Dimensional Testing and Inference Type de document : document électronique Auteurs : Zheng Gao, ; Stilian Stoev, ; SpringerLink (Online service) Editeur : Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer Année de publication : 2021 Collection : SpringerBriefs in Probability and Mathematical Statistics, ISSN 2365-4333 Importance : XIII, 140 p. 12 illus., 2 illus. in color Présentation : online resource ISBN/ISSN/EAN : 978-3-030-80964-5 Langues : Anglais (eng) Tags : Probabilities Statistics Probability Theory and Stochastic Processes Statistics general Résumé : This book provides a unified exposition of some fundamental theoretical problems in high-dimensional statistics. It specifically considers the canonical problems of detection and support estimation for sparse signals observed with noise. Novel phase-transition results are obtained for the signal support estimation problem under a variety of statistical risks. Based on a surprising connection to a concentration of maxima probabilistic phenomenon, the authors obtain a complete characterization of the exact support recovery problem for thresholding estimators under dependent errors. Note de contenu : Chapter 1 Introduction and Guiding Examples -- Chapter 2 Risks, Procedures, and Error Models -- Chapter 3 A Panorama of Phase Transitions -- Chapter 4 Exact Support Recovery Under Dependence -- Chapter 5 Bayes and Minimax Optimality -- Chapter 6 Uniform Relative Stability for Gaussian Array -- Chapter 7 Fundamental Statistical Limits in Genome-wide Association Studies -- References -- Additional proofs -- Exact support recovery in non AGG models Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=166064 Concentration of Maxima and Fundamental Limits in High-Dimensional Testing and Inference [document électronique] / Zheng Gao, ; Stilian Stoev, ; SpringerLink (Online service) . - Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer, 2021 . - XIII, 140 p. 12 illus., 2 illus. in color : online resource. - (SpringerBriefs in Probability and Mathematical Statistics, ISSN 2365-4333) .
ISBN : 978-3-030-80964-5
Langues : Anglais (eng)
Tags : Probabilities Statistics Probability Theory and Stochastic Processes Statistics general Résumé : This book provides a unified exposition of some fundamental theoretical problems in high-dimensional statistics. It specifically considers the canonical problems of detection and support estimation for sparse signals observed with noise. Novel phase-transition results are obtained for the signal support estimation problem under a variety of statistical risks. Based on a surprising connection to a concentration of maxima probabilistic phenomenon, the authors obtain a complete characterization of the exact support recovery problem for thresholding estimators under dependent errors. Note de contenu : Chapter 1 Introduction and Guiding Examples -- Chapter 2 Risks, Procedures, and Error Models -- Chapter 3 A Panorama of Phase Transitions -- Chapter 4 Exact Support Recovery Under Dependence -- Chapter 5 Bayes and Minimax Optimality -- Chapter 6 Uniform Relative Stability for Gaussian Array -- Chapter 7 Fundamental Statistical Limits in Genome-wide Association Studies -- References -- Additional proofs -- Exact support recovery in non AGG models Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=166064 Lectures on Random Interfaces / Tadahisa Funaki / Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer (2016)
Titre : Lectures on Random Interfaces Type de document : document électronique Auteurs : Tadahisa Funaki ; SpringerLink (Online service) Editeur : Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer Année de publication : 2016 Collection : SpringerBriefs in Probability and Mathematical Statistics, ISSN 2365-4333 Importance : XII, 138 p. 44 illus., 9 illus. in color Présentation : online resource ISBN/ISSN/EAN : 978-981-10-0849-8 Langues : Anglais (eng) Tags : Mathematics Partial differential equations Probabilities Mathematical physics Probability Theory and Stochastic Processes Partial Differential Equations Mathematical Physics Résumé : Interfaces are created to separate two distinct phases in a situation in which phase coexistence occurs. This book discusses randomly fluctuating interfaces in several different settings and from several points of view: discrete/continuum, microscopic/macroscopic, and static/dynamic theories. The following four topics in particular are dealt with in the book. Assuming that the interface is represented as a height function measured from a fixed-reference discretized hyperplane, the system is governed by the Hamiltonian of gradient of the height functions. This is a kind of effective interface model called ??-interface model. The scaling limits are studied for Gaussian (or non-Gaussian) random fields with a pinning effect under a situation in which the rate functional of the corresponding large deviation principle has non-unique minimizers. Young diagrams determine decreasing interfaces, and their dynamics are introduced. The large-scale behavior of such dynamics is studied from the points of view of the hydrodynamic limit and non-equilibrium fluctuation theory. Vershik curves are derived in that limit. A sharp interface limit for the Allen?Cahn equation, that is, a reaction?diffusion equation with bistable reaction term, leads to a mean curvature flow for the interfaces. Its stochastic perturbation, sometimes called a time-dependent Ginzburg?Landau model, stochastic quantization, or dynamic P(?)-model, is considered. Brief introductions to Brownian motions, martingales, and stochastic integrals are given in an infinite dimensional setting. The regularity property of solutions of stochastic PDEs (SPDEs) of a parabolic type with additive noises is also discussed. The Kardar?Parisi?Zhang (KPZ) equation , which describes a growing interface with fluctuation, recently has attracted much attention. This is an ill-posed SPDE and requires a renormalization. Especially its invariant measures are studied. Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=124370 Lectures on Random Interfaces [document électronique] / Tadahisa Funaki ; SpringerLink (Online service) . - Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer, 2016 . - XII, 138 p. 44 illus., 9 illus. in color : online resource. - (SpringerBriefs in Probability and Mathematical Statistics, ISSN 2365-4333) .
ISBN : 978-981-10-0849-8
Langues : Anglais (eng)
Tags : Mathematics Partial differential equations Probabilities Mathematical physics Probability Theory and Stochastic Processes Partial Differential Equations Mathematical Physics Résumé : Interfaces are created to separate two distinct phases in a situation in which phase coexistence occurs. This book discusses randomly fluctuating interfaces in several different settings and from several points of view: discrete/continuum, microscopic/macroscopic, and static/dynamic theories. The following four topics in particular are dealt with in the book. Assuming that the interface is represented as a height function measured from a fixed-reference discretized hyperplane, the system is governed by the Hamiltonian of gradient of the height functions. This is a kind of effective interface model called ??-interface model. The scaling limits are studied for Gaussian (or non-Gaussian) random fields with a pinning effect under a situation in which the rate functional of the corresponding large deviation principle has non-unique minimizers. Young diagrams determine decreasing interfaces, and their dynamics are introduced. The large-scale behavior of such dynamics is studied from the points of view of the hydrodynamic limit and non-equilibrium fluctuation theory. Vershik curves are derived in that limit. A sharp interface limit for the Allen?Cahn equation, that is, a reaction?diffusion equation with bistable reaction term, leads to a mean curvature flow for the interfaces. Its stochastic perturbation, sometimes called a time-dependent Ginzburg?Landau model, stochastic quantization, or dynamic P(?)-model, is considered. Brief introductions to Brownian motions, martingales, and stochastic integrals are given in an infinite dimensional setting. The regularity property of solutions of stochastic PDEs (SPDEs) of a parabolic type with additive noises is also discussed. The Kardar?Parisi?Zhang (KPZ) equation , which describes a growing interface with fluctuation, recently has attracted much attention. This is an ill-posed SPDE and requires a renormalization. Especially its invariant measures are studied. Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=124370 Mod-? Convergence / Valentin Féray / Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer (2016)
PermalinkNonlinearly Perturbed Semi-Markov Processes / Dmitrii S. Silvestrov / Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer (2017)
PermalinkOn Stein's Method for Infinitely Divisible Laws with Finite First Moment / Benjamin Arras / Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer (2019)
PermalinkPath Coupling and Aggregate Path Coupling / Yevgeniy Kovchegov / Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer (2018)
PermalinkPoisson Point Processes and Their Application to Markov Processes / Kiyosi Itô / Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer (2015)
PermalinkRegularity and Irregularity of Superprocesses with (1 + ?)-stable Branching Mechanism / Leonid Mytnik / Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer (2016)
PermalinkStable Non-Gaussian Self-Similar Processes with Stationary Increments / Vladas Pipiras / Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer (2017)
PermalinkTopics in Infinitely Divisible Distributions and Lévy Processes, Revised Edition / Alfonso Rocha-Arteaga / Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer (2019)
PermalinkZero-Sum Discrete-Time Markov Games with Unknown Disturbance Distribution / J. Adolfo Minjárez-Sosa / Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer (2020)
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