Weak Solutions of Stochastic Differential Equations over the Field of p-Adic Numbers

Details Weak Solutions of Stochastic Differential Equations over the Field of p-Adic Numbers Weak Solutions of Stochastic Differential Equations over the Field of p-Adic Numbers

2007-08-13

arxiv.org/abs/0708.1706v1

Mathematics

Probability

To appear in Tohoku Math. J

Scientific paper

Study of stochastic differential equations on the field of p-adic numbers was initiated by the second author and has been developed by the first author, who proved several results for the p-adic case, similar to the theory of ordinary stochastic integral with respect to Levy processes on the Euclidean spaces. In this article, we present an improved definition of a stochastic integral on the field and prove the joint (time and space) continuity of the local time for p-adic stable processes. Then we use the method of random time change to obtain sufficient conditions for the existence of a weak solution of a stochastic differential equation on the field, driven by the p-adic stable process, with a Borel measurable coefficient.

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