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Measure Valued Processes And Stochastic Flows

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Measure Valued Processes And Stochastic Flows

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Author : Andrey A. Dorogovtsev
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2023-11-06

Measure Valued Processes And Stochastic Flows written by Andrey A. Dorogovtsev and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-06 with Mathematics categories.

This book discusses the systems of interacting particles evolving in the random media. The focus is on the study of both the finite subsystems motion and the flow, describing motion of all particles in the space. The integral characteristics of the system and mass distribution are also covered and results are illustrated with examples from turbulence theory, synchronization and DNA evolution.

Measure Valued Processes And Stochastic Flows

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Author : Andrey A. Dorogovtsev
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2023-11-06

Measure Valued Branching Markov Processes

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Author : Zenghu Li
language : en
Publisher: Springer Nature
Release Date : 2023-03-13

Measure Valued Branching Markov Processes written by Zenghu Li and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-13 with Mathematics categories.

This book provides a compact introduction to the theory of measure-valued branching processes, immigration processes and Ornstein–Uhlenbeck type processes. Measure-valued branching processes arise as high density limits of branching particle systems. The first part of the book gives an analytic construction of a special class of such processes, the Dawson–Watanabe superprocesses, which includes the finite-dimensional continuous-state branching process as an example. Under natural assumptions, it is shown that the superprocesses have Borel right realizations. Transformations are then used to derive the existence and regularity of several different forms of the superprocesses. This technique simplifies the constructions and gives useful new perspectives. Martingale problems of superprocesses are discussed under Feller type assumptions. The second part investigates immigration structures associated with the measure-valued branching processes. The structures are formulated by skew convolution semigroups, which are characterized in terms of infinitely divisible probability entrance laws. A theory of stochastic equations for one-dimensional continuous-state branching processes with or without immigration is developed, which plays a key role in the construction of measure flows of those processes. The third part of the book studies a class of Ornstein-Uhlenbeck type processes in Hilbert spaces defined by generalized Mehler semigroups, which arise naturally in fluctuation limit theorems of the immigration superprocesses. This volume is aimed at researchers in measure-valued processes, branching processes, stochastic analysis, biological and genetic models, and graduate students in probability theory and stochastic processes.

Measure Valued Branching Markov Processes

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Author : Zenghu Li
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-10

Measure Valued Branching Markov Processes written by Zenghu Li and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-10 with Mathematics categories.

Measure-valued branching processes arise as high density limits of branching particle systems. The Dawson-Watanabe superprocess is a special class of those. The author constructs superprocesses with Borel right underlying motions and general branching mechanisms and shows the existence of their Borel right realizations. He then uses transformations to derive the existence and regularity of several different forms of the superprocesses. This treatment simplifies the constructions and gives useful perspectives. Martingale problems of superprocesses are discussed under Feller type assumptions. The most important feature of the book is the systematic treatment of immigration superprocesses and generalized Ornstein--Uhlenbeck processes based on skew convolution semigroups. The volume addresses researchers in measure-valued processes, branching processes, stochastic analysis, biological and genetic models, and graduate students in probability theory and stochastic processes.

Stochastic Flows In The Brownian Web And Net

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Author : Emmanuel Schertzer
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-01-08

Stochastic Flows In The Brownian Web And Net written by Emmanuel Schertzer and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-08 with Mathematics categories.

It is known that certain one-dimensional nearest-neighbor random walks in i.i.d. random space-time environments have diffusive scaling limits. Here, in the continuum limit, the random environment is represented by a `stochastic flow of kernels', which is a collection of random kernels that can be loosely interpreted as the transition probabilities of a Markov process in a random environment. The theory of stochastic flows of kernels was first developed by Le Jan and Raimond, who showed that each such flow is characterized by its -point motions. The authors' work focuses on a class of stochastic flows of kernels with Brownian -point motions which, after their inventors, will be called Howitt-Warren flows. The authors' main result gives a graphical construction of general Howitt-Warren flows, where the underlying random environment takes on the form of a suitably marked Brownian web. This extends earlier work of Howitt and Warren who showed that a special case, the so-called "erosion flow", can be constructed from two coupled "sticky Brownian webs". The authors' construction for general Howitt-Warren flows is based on a Poisson marking procedure developed by Newman, Ravishankar and Schertzer for the Brownian web. Alternatively, the authors show that a special subclass of the Howitt-Warren flows can be constructed as random flows of mass in a Brownian net, introduced by Sun and Swart. Using these constructions, the authors prove some new results for the Howitt-Warren flows.

Qualitative And Asymptotic Analysis Of Differential Equations With Random Perturbations

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Author : Anatoliy M Samoilenko
language : en
Publisher: World Scientific
Release Date : 2011-06-07

Qualitative And Asymptotic Analysis Of Differential Equations With Random Perturbations written by Anatoliy M Samoilenko and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-07 with Mathematics categories.

Differential equations with random perturbations are the mathematical models of real-world processes that cannot be described via deterministic laws, and their evolution depends on random factors. The modern theory of differential equations with random perturbations is on the edge of two mathematical disciplines: random processes and ordinary differential equations. Consequently, the sources of these methods come both from the theory of random processes and from the classic theory of differential equations.This work focuses on the approach to stochastic equations from the perspective of ordinary differential equations. For this purpose, both asymptotic and qualitative methods which appeared in the classical theory of differential equations and nonlinear mechanics are developed.

From Probability To Finance

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Author : Ying Jiao
language : en
Publisher: Springer Nature
Release Date : 2020-03-20

From Probability To Finance written by Ying Jiao and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-20 with Mathematics categories.

This volume presents a collection of lecture notes of mini-courses taught at BICMR Summer School of Financial Mathematics, from May 29 to June 9, 2017. Each chapter is self-contained and corresponds to one mini-course which deals with a distinguished topic, such as branching processes, enlargement of filtrations, Hawkes processes, copula models and valuation adjustment analysis, whereas the global topics cover a wide range of advanced subjects in financial mathematics, from both theoretical and practical points of view. The authors include world-leading specialists in the domain and also young active researchers. This book will be helpful for students and those who work on probability and financial mathematics.

Stochastic Analysis

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Author : Kiyosi Itō
language : en
Publisher: Elsevier
Release Date : 1984

Stochastic Analysis written by Kiyosi Itō and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.

Stochastic analysis, a branch of probability theory stemming from the theory of stochastic differential equations, is becoming increasingly important in connection with partial differential equations, non-linear functional analysis, control theory and statistical mechanics.

Diffusion Processes And Related Problems In Analysis Volume Ii

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Author : V. Wihstutz
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Diffusion Processes And Related Problems In Analysis Volume Ii written by V. Wihstutz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

During the weekend of March 16-18, 1990 the University of North Carolina at Charlotte hosted a conference on the subject of stochastic flows, as part of a Special Activity Month in the Department of Mathematics. This conference was supported jointly by a National Science Foundation grant and by the University of North Carolina at Charlotte. Originally conceived as a regional conference for researchers in the Southeastern United States, the conference eventually drew participation from both coasts of the U. S. and from abroad. This broad-based par ticipation reflects a growing interest in the viewpoint of stochastic flows, particularly in probability theory and more generally in mathematics as a whole. While the theory of deterministic flows can be considered classical, the stochastic counterpart has only been developed in the past decade, through the efforts of Harris, Kunita, Elworthy, Baxendale and others. Much of this work was done in close connection with the theory of diffusion processes, where dynamical systems implicitly enter probability theory by means of stochastic differential equations. In this regard, the Charlotte conference served as a natural outgrowth of the Conference on Diffusion Processes, held at Northwestern University, Evanston Illinois in October 1989, the proceedings of which has now been published as Volume I of the current series. Due to this natural flow of ideas, and with the assistance and support of the Editorial Board, it was decided to organize the present two-volume effort.

Stochastic Spatial Processes

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Author : Petre Tautu
language : en
Publisher: Springer
Release Date : 2006-11-14

Stochastic Spatial Processes written by Petre Tautu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

Proceedings of a Conference held in Heidelberg, September 10 - 14, 1984

Measure Valued Processes And Stochastic Flows

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