Qp-valued jump processes associated with linear and nonlinear pseudo-differential equations

Abstract

We consider stochastic differential equations in the space Qp of p-adic numbers associated with nonlinear pseudo-differential equations and systems. We construct both scalar and matrix-valued multiplicative functionals of Qp-valued Markov processes and derive probabilistic representations of solutions to the Cauchy problem for nonlinear pseudo-differential equations and systems which extend the Feynman-Kac formula. Bibliography: 12 titles.