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Author: Andrey A. Dorogovtsev
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110986515
Category : Mathematics
Languages : en
Pages : 228
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Book Description
Author: Andrey A. Dorogovtsev
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110986515
Category : Mathematics
Languages : en
Pages : 228
Get Book Here
Book Description
Author: Andrey A. Dorogovtsev
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110986558
Category : Mathematics
Languages : en
Pages : 295
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Book Description
Author: H. Kunita
Publisher:
ISBN:
Category : Flows (Differentiable dynamical systems).
Languages : en
Pages : 184
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Book Description
Author: Zenghu Li
Publisher: Springer Nature
ISBN: 3662669102
Category : Mathematics
Languages : en
Pages : 481
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Book Description
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.
Author: Emmanuel Schertzer
Publisher: American Mathematical Soc.
ISBN: 0821890883
Category : Mathematics
Languages : en
Pages : 172
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Book Description
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.
Author: Fabrice Baudoin
Publisher: World Scientific
ISBN: 1860944817
Category : Mathematics
Languages : en
Pages : 152
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Book Description
This book aims to provide a self-contained introduction to the local geometry of the stochastic flows associated with stochastic differential equations. It stresses the view that the local geometry of any stochastic flow is determined very precisely and explicitly by a universal formula referred to as the Chen-Strichartz formula. The natural geometry associated with the Chen-Strichartz formula is the sub-Riemannian geometry whose main tools are introduced throughout the text. By using the connection between stochastic flows and partial differential equations, we apply this point of view of the study of hypoelliptic operators written in Hormander's form.
Author: Donald A. Dawson
Publisher: Springer
ISBN: 3540476083
Category : Mathematics
Languages : en
Pages : 362
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Book Description
CONTENTS: D.D. Dawson: Measure-valued Markov Processes.- B. Maisonneuve: Processus de Markov: Naissance, Retournement, Regeneration.- J. Spencer: Nine lectures on Random Graphs.
Author: Amitava Bose
Publisher:
ISBN:
Category : Stochastic processes
Languages : en
Pages : 304
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Book Description
Author: R. W. R. Darling
Publisher: American Mathematical Soc.
ISBN: 0821824392
Category : Mathematics
Languages : en
Pages : 109
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Book Description
The purpose of this article is the construction of stochastic flows from the finite-dimensional distributions without any smoothness assumptions. Also examines the relation between covariance functions and finite-dimensional distributions. The stochastic continuity of stochastic flows in the time parameter are proved in each section. These results give some extensions of the results obtained by Harris, by Baxendale and Harris and by other authors. In particular, the author studies coalescing flows, which were introduced by Harris for the study of flows of nonsmooth maps.
Author: Avner Friedman
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 360
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Book Description
Optimal stopping in a reliability problem; On the Hamilton-Jacobi approach for the optimal control of diffusion processes with Jumps; On the number of distinct sites visited by a Random Walk; Duality for markov processes; Stochastic dynamical systems and their flows; Some measure-valued population processes; Optimal stopping for random evolution of multidimensional poisson processes with partial observation; The tail 0-field of one dimensional diffusions.
