Stochastic processes and antiderivational equations on non-Archimedean manifolds
type: Item
instance of: scholarly article
title: Stochastic processes and antiderivational equations on non-Archimedean manifolds
zbMATH Open document ID: 1094.60022
DOI: 10.1155/S016117120421225X
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2005-05-18T00:00:00Z
full work available at URL: https://eudml.org/doc/52618
review text: This work is a continuation of the author's previous papers [Int. J. Math. Math. Sci. 2003, No. 21, 1341--1363 (2003; Zbl 1076.60045); ibid. 2003, No. 41, 2587--2602 (2003; Zbl 1095.60014)], in which he constructed certain classes of measures on Banach spaces over non-Archimedean local fields. Using those results, now he studies stochastic differential equations on manifolds modeled on the above spaces. The processes under consideration have both the time parameter and values from non-Archimedean spaces. As in the above papers, the approach is based on a non-Archimedean analog of the Gaussian measure defined on cylindrical sets as a product of one-dimensional weighted Haar measures, with weights resembling formally the classical ones. This notion of the Gaussian measure is different from a more refined one, proposed by \textit{S. N. Evans} [in: Topics in probability and Lie groups: Boundary theory. CRM Proc. Lect. Notes 28, 11--50 (2001; Zbl 0989.60039)]. Another important tool is \textit{W. H. Schikhof}'s antiderivative of a function of a \(p\)-adic argument [``Ultrametric calculus. An introduction to \(p\)-adic analysis'' (1984; Zbl 0553.26006)].
reviewed by: Anatoly N. Kochubei
Mathematics Subject Classification ID: 60G05
Mathematics Subject Classification ID: 58J65
Mathematics Subject Classification ID: 46S10
zbMATH DE Number: 2168715
zbMATH Keywords: infinite-dimensional manifold over a local field
zbMATH Keywords: stochastic differential equation
author: Sergey V. Ludkovsky
MaRDI profile type: Publication
OpenAlex ID: W1978231833
description: scientific article; zbMATH DE number 2168715