SpringerBriefs in Probability and Mathematical Statistics (47 Ergebnisse)

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Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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, italso provides anaccessible introduction to the fundamentals of this current topic, as well as an overview thatwill serve as an invitation and catalyst for further research. Statistics in Wasserstein spaces represents an emerging topic inmathematical statistics, situated at the interface between functional dataanalysis (where the data are functions, thus lying in infinite dimensionalHilbert space) and non-Euclidean statistics (where the data satisfy nonlinearconstraints, thus lying on non-Euclidean manifolds). The Wassersteinspace provides the natural mathematical formalism to describe datacollections that are best modeled as random measures on Euclidean space (e.g. imagesand point processes). Such random measures carry the infinite dimensionaltraits of functional data, but are intrinsically nonlinear due to positivity andintegrability restrictions. Indeed, their dominating statistical variationarises through random deformations of an underlying template, a theme that is pursued in depth in this monograph.

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Taschenbuch. Zustand: Neu. An Invitation to Statistics in Wasserstein Space | Victor M. Panaretos (u. a.) | Taschenbuch | Einband - flex.(Paperback) | Englisch | 2020 | Springer | EAN 9783030384371 | Verantwortliche Person für die EU: Springer-Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, productsafety[at]springernature[dot]com | Anbieter: preigu.

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Kartoniert / Broschiert. Zustand: New. First of its kind publication detailing the mod-? convergence methodWritten by leading experts in probability theoryProvides a large number of new resultsIncludes new e.

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Taschenbuch. Zustand: Neu. Neuware -This SpringerBrief deals with a class of discrete-time zero-sum Markov games with Borel state and action spaces, and possibly unbounded payoffs, under discounted and average criteria, whose state process evolves according to a stochastic difference equation. The corresponding disturbance process is an observable sequence of independent and identically distributed random variables with unknown distribution for both players. Unlike the standard case, the game is played over an infinite horizon evolving as follows. At each stage, once the players have observed the state of the game, and before choosing the actions, players 1 and 2 implement a statistical estimation process to obtain estimates of the unknown distribution. Then, independently, the players adapt their decisions to such estimators to select their actions and construct their strategies. This book presents a systematic analysis on recent developments in this kind of games. Specifically, the theoretical foundations on the procedures combining statistical estimation and control techniques for the construction of strategies of the players are introduced, with illustrative examples. In this sense, the book is an essential reference for theoretical and applied researchers in the fields of stochastic control and game theory, and their applications.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 136 pp. Englisch.

Taschenbuch. Zustand: Neu. Neuware -An extension problem (often called a boundary problem) of Markov processes has been studied, particularly in the case of one-dimensional diffusion processes, by W. Feller, K. Itô, and H. P. McKean, among others. In this book, Itô discussed a case of a general Markov process with state space S and a specified point a ¿ Scalled a boundary. The problem is to obtain all possible recurrent extensions of a given minimal process(i.e., the process on S {a} which is absorbed on reaching the boundary a). The study in this lecture is restricted to a simpler case of the boundary a being a discontinuous entrance point, leaving a more general case of a continuous entrance point to future works. He established a one-to-one correspondence between a recurrent extension and a pair of a positive measure k(db) onS{a}(called the jumping-in measure and a non-negative number mSpringer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 56 pp. Englisch.

Taschenbuch. Zustand: Neu. Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 152 pp. Englisch.

Taschenbuch. Zustand: Neu. Neuware -The book presents new methods of asymptotic analysis for nonlinearly perturbed semi-Markov processes with a finite phase space. These methods are based on special time-space screening procedures for sequential phase space reduction of semi-Markov processes combined with the systematical use of operational calculus for Laurent asymptotic expansions. Effective recurrent algorithms are composed for getting asymptotic expansions, without and with explicit upper bounds for remainders, for power moments of hitting times, stationary and conditional quasi-stationary distributions for nonlinearly perturbed semi-Markov processes. These results are illustrated by asymptotic expansions for birth-death-type semi-Markov processes, which play an important role in various applications. The book will be a useful contribution to the continuing intensive studies in the area. It is an essential reference for theoretical and applied researchersin the field of stochastic processes and their applications that will contribute to continuing extensive studies in the area and remain relevant for years to come.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 160 pp. Englisch.

Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - This is the only book discussing multifractal properties of densities of stable superprocesses, containing latest achievements while also givingthe reader a comprehensive picture of the state of the art in this area. It is a self-contained presentation of regularity properties of stablesuperprocesses and proofs of main results and can serve as an introductory text for a graduate course. There are many heuristic explanations of technically involved results and proofs and the reader can get a clear intuitive picture behind the results and techniques.

Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - The book presents new methods of asymptotic analysis fornonlinearly perturbed semi-Markov processes with a finite phasespace. These methods are based on special time-space screeningprocedures for sequential phase space reduction of semi-Markov processes combined with the systematical use of operationalcalculus for Laurent asymptotic expansions. Effective recurrentalgorithms are composed for getting asymptotic expansions, withoutand with explicit upper bounds for remainders, for power moments ofhitting times, stationary and conditional quasi-stationary distributionsfor nonlinearly perturbed semi-Markov processes. These results areillustrated by asymptotic expansions for birth-death-type semi-Markov processes, which play an important role in variousapplications. The book will be a useful contribution to the continuingintensive studies in the area. It is an essential reference for theoreticaland applied researchersin the field of stochastic processes and their applications that will contribute to continuing extensive studies in thearea and remain relevant for years to come.

Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - This SpringerBriefdeals with a class of discrete-time zero-sum Markov games with Borel state and action spaces, and possibly unbounded payoffs, under discounted and average criteria, whose state process evolves according to a stochastic difference equation. The corresponding disturbance process is an observable sequence of independent and identically distributed random variables with unknown distribution for both players. Unlike the standard case, the game is played over an infinite horizon evolving as follows. At each stage, once the players have observed the state of the game, and before choosing the actions, players 1 and 2 implement a statistical estimation process to obtain estimates of the unknown distribution. Then, independently, the players adapt their decisions to such estimators to select their actions and construct their strategies. This book presents a systematic analysis on recent developments in this kind of games. Specifically, the theoretical foundations on the procedures combining statistical estimation and control techniques for the construction of strategies of the players are introduced, with illustrative examples. In this sense, the book is an essential reference for theoretical and applied researchers in the fields of stochastic control and game theory, and their applications.

Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - This book provides a self-contained presentation on the structure of a large class of stable processes, known as self-similar mixed moving averages. The authors present a way to describe and classify these processes by relating them to so-called deterministic flows. The first sections in the book review random variables, stochastic processes, and integrals, moving on to rigidity and flows, and finally ending with mixed moving averages and self-similarity. In-depth appendices are also included. This book is aimed at graduate students and researchers working in probability theory and statistics.

Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - The canonical way to establish the central limit theorem for i.i.d. random variables is to use characteristic functions and Lévy's continuity theorem. This monograph focuses on this characteristic function approach and presents a renormalization theory called mod- convergence. This type of convergence is a relatively new concept with many deep ramifications, and has not previously been published in a single accessible volume. The authors construct an extremely flexible framework using this concept in order to study limit theorems and large deviations for a number of probabilistic models related to classical probability, combinatorics, non-commutative random variables, as well as geometric and number-theoretical objects.Intended for researchers in probability theory, the text is carefully well-written and well-structured, containing a great amount of detail and interesting examples.

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Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - This book describes and characterizes an extension to the classical path coupling method applied to statistical mechanical models, referred to as aggregate path coupling. In conjunction with large deviations estimates, the aggregate path coupling method is used to prove rapid mixing of Glauber dynamics for a large class of statistical mechanical models, including models that exhibit discontinuous phase transitions which have traditionally been more difficult to analyze rigorously. The book shows how the parameter regions for rapid mixing for several classes of statistical mechanical models are derived using the aggregate path coupling method.

Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - An extension problem (often called a boundary problem) of Markov processes has been studied, particularly in the case of one-dimensional diffusion processes, by W. Feller, K. Itô, and H. P. McKean, among others. In this book, Itô discussed a case of a general Markov process with state space S and a specified point a S called a boundary. The problem is to obtain all possible recurrent extensions of a given minimal process (i.e., the process on S {a} which is absorbed on reaching the boundary a). The study in this lecture is restricted to a simpler case of the boundary a being a discontinuous entrance point, leaving a more general case of a continuous entrance point to future works. He established a one-to-one correspondence between a recurrent extension and a pair of a positive measure k(db) on S {a} (called the jumping-in measure and a non-negative number m< (called the stagnancy rate). The necessary and sufficient conditions for a pair k, m was obtained so that the correspondence is precisely described. For this, Itô used, as a fundamental tool, the notion of Poisson point processes formed of all excursions of the process on S {a}. This theory of Itô's of Poisson point processes of excursions is indeed a breakthrough. It has been expanded and applied to more general extension problems by many succeeding researchers. Thus we may say that this lecture note by Itô is really a memorial work in the extension problems of Markov processes. Especially in Chapter 1 of this note, a general theory of Poisson point processes is given that reminds us of Itô's beautiful and impressive lectures in his day.

Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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 phi-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 dynamicsis 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(phi)-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.