Weak solutions of stochastic differential equations over the field of $p$-adic numbers
Kaneko, Hiroshi ; Kochubei, Anatoly N.
Tohoku Math. J. (2), Tome 59 (2007) no. 1, p. 547-564 / Harvested from Project Euclid
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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.
Publié le : 2007-05-15
Classification:  60H10,  11S80,  60G52 
@article{1199649874,
     author = {Kaneko, Hiroshi and Kochubei, Anatoly N.},
     title = {Weak solutions of stochastic differential equations over the field of $p$-adic
				numbers},
     journal = {Tohoku Math. J. (2)},
     volume = {59},
     number = {1},
     year = {2007},
     pages = { 547-564},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1199649874}
}

Kaneko, Hiroshi; Kochubei, Anatoly N. Weak solutions of stochastic differential equations over the field of $p$-adic
				numbers. Tohoku Math. J. (2), Tome 59 (2007) no. 1, pp.  547-564. http://gdmltest.u-ga.fr/item/1199649874/