Stochastic antiderivational equations on non-Archimedean Banach spaces
This work is a continuation of the previous author's paper [Int. J. Math. Math. Sci. 2003, No. 21, 1341--1363 (2003; Zbl 1076.60045)]. The author introduces 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. Using this measure he defines a Wiener process with \(p\)-adic time, introduces and investigates an analog of a stochastic differential equation based on Schikhof's antiderivative of a function of a \(p\)-adic argument. An existence and uniqueness theorem is proved. Note that there exists a different approach to Gaussian measures on linear spaces over non-Archimedean fields also leading to a kind of a Wiener process, with deeper probabilistic properties. See the papers 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); J. Theor. Probab. 6, 817-850 (1993; Zbl 0803.60078) and in: Probability measures on groups and related structures XI, 102--115 (1995; Zbl 0911.60034)].
scientific article; zbMATH DE number 2012561