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2007 Weak solutions of stochastic differential equations over the field of $p$-adic numbers
Hiroshi Kaneko, Anatoly N. Kochubei
Tohoku Math. J. (2) 59(4): 547-564 (2007). DOI: 10.2748/tmj/1199649874

Abstract

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 Lévy processes on 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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Hiroshi Kaneko. Anatoly N. Kochubei. "Weak solutions of stochastic differential equations over the field of $p$-adic numbers." Tohoku Math. J. (2) 59 (4) 547 - 564, 2007. https://doi.org/10.2748/tmj/1199649874

Information

Published: 2007
First available in Project Euclid: 6 January 2008

zbMATH: 1136.60039
MathSciNet: MR2404205
Digital Object Identifier: 10.2748/tmj/1199649874

Subjects:
Primary: 60H10
Secondary: 11S80, 60G52

Rights: Copyright © 2007 Tohoku University

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Vol.59 • No. 4 • 2007
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