Jump processes in $Q_p$ associated with nonlinear pseudo-differential equations

We consider stochastic differential equations in the space $Q_p$ of $p-$adic numbers which associated with nonlinear pseudo-differential equations and systems of such equations. To this end we construct both scalar and matrix valued multiplicative functionals of $Q_p$-valued Markov processes and derive the probabilistic representations of the Cauchy problem solutions for nonlinear pseudo-differential equations and systems which extend the Feynman–Kac formula.