Stochastic flows and sticky Brownian motion
Author : Christopher John Howitt
Publisher :
Page : 0 pages
File Size : 22,60 MB
Release : 2007
Category :
ISBN :
Author : Christopher John Howitt
Publisher :
Page : 0 pages
File Size : 22,60 MB
Release : 2007
Category :
ISBN :
Author : Emmanuel Schertzer
Publisher : American Mathematical Soc.
Page : 172 pages
File Size : 37,91 MB
Release : 2014-01-08
Category : Mathematics
ISBN : 0821890883
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 : Christopher John Howitt
Publisher :
Page : 233 pages
File Size : 13,86 MB
Release : 2007
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Author : Neslihan Şahin
Publisher :
Page : 68 pages
File Size : 19,25 MB
Release : 2017
Category : Brownian motion processes
ISBN :
Author : R. W. R. Darling
Publisher : American Mathematical Soc.
Page : 109 pages
File Size : 16,67 MB
Release : 1987
Category : Mathematics
ISBN : 0821824392
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 : René L. Schilling
Publisher : Walter de Gruyter GmbH & Co KG
Page : 514 pages
File Size : 32,73 MB
Release : 2014-08-22
Category : Mathematics
ISBN : 311037398X
Brownian motion is one of the most important stochastic processes in continuous time and with continuous state space. Within the realm of stochastic processes, Brownian motion is at the intersection of Gaussian processes, martingales, Markov processes, diffusions and random fractals, and it has influenced the study of these topics. Its central position within mathematics is matched by numerous applications in science, engineering and mathematical finance. Often textbooks on probability theory cover, if at all, Brownian motion only briefly. On the other hand, there is a considerable gap to more specialized texts on Brownian motion which is not so easy to overcome for the novice. The authors’ aim was to write a book which can be used as an introduction to Brownian motion and stochastic calculus, and as a first course in continuous-time and continuous-state Markov processes. They also wanted to have a text which would be both a readily accessible mathematical back-up for contemporary applications (such as mathematical finance) and a foundation to get easy access to advanced monographs. This textbook, tailored to the needs of graduate and advanced undergraduate students, covers Brownian motion, starting from its elementary properties, certain distributional aspects, path properties, and leading to stochastic calculus based on Brownian motion. It also includes numerical recipes for the simulation of Brownian motion.
Author : René L. Schilling
Publisher : Walter de Gruyter GmbH & Co KG
Page : 533 pages
File Size : 49,25 MB
Release : 2021-09-07
Category : Mathematics
ISBN : 311074127X
Stochastic processes occur everywhere in the sciences, economics and engineering, and they need to be understood by (applied) mathematicians, engineers and scientists alike. This book gives a gentle introduction to Brownian motion and stochastic processes, in general. Brownian motion plays a special role, since it shaped the whole subject, displays most random phenomena while being still easy to treat, and is used in many real-life models. Im this new edition, much material is added, and there are new chapters on ''Wiener Chaos and Iterated Itô Integrals'' and ''Brownian Local Times''.
Author : Ananda Pathirannehelage Nihal Weerasinghe
Publisher :
Page : 220 pages
File Size : 36,74 MB
Release : 1986
Category :
ISBN :
Author : J. Michael Harrison
Publisher : Krieger Publishing Company
Page : 140 pages
File Size : 39,7 MB
Release : 1985
Category : Mathematics
ISBN : 9780894644559
Author : René L. Schilling
Publisher : de Gruyter
Page : 0 pages
File Size : 48,87 MB
Release : 2012
Category : MATHEMATICS
ISBN : 9783110278897
Stochastic processes occur in a large number of fields in sciences and engineering, so they need to be understood by applied mathematicians, engineers and scientists alike. This work is ideal for a first course introducing the reader gently to the subject matter of stochastic processes. It uses Brownian motion since this is a stochastic process which is central to many applications and which allows for a treatment without too many technicalities. All chapters are modular and are written in a style where the lecturer can ""pick and mix"" topics. A ""dependence chart"" will guide the reader when.