Stochastic processes and antiderivational equations on non-Archimedean manifolds
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)].
infinite-dimensional manifold over a local field
scientific article; zbMATH DE number 2168715