Geodesic
Jump processes in $Q_p$ associated with nonlinear pseudo-differential equations
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 12, Tome 351 (2007), pp. 5-37

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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. 
@article{ZNSL_2007_351_a0,
     author = {S. A. Albeverio and Ya. I. Belopol'skaya},
     title = {Jump processes in $Q_p$ associated with nonlinear pseudo-differential equations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--37},
     publisher = {mathdoc},
     volume = {351},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_351_a0/}
}
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S. A. Albeverio; Ya. I. Belopol'skaya. Jump processes in $Q_p$ associated with nonlinear pseudo-differential equations. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 12, Tome 351 (2007), pp. 5-37. http://geodesic.mathdoc.fr/item/ZNSL_2007_351_a0/