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

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

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.
To appear in Tohoku Math. J

Keywords

Probability, Number Theory, 60H10 (Primary); 11S80, 60G52 (Secondary)

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/135986

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0708.1706
 http://arxiv.org/abs/0708.1706

Collections

arXiv