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Approximations of solutions of stochastic differential equations driven by semimartingales. (English) Zbl 0578.60055

Author’s abstract: The classical results on the instability of the solutions of stochastic differential equations are extended in two directions: the coefficients are allowed to depend on the paths of the solutions, and arbitrary semimartingales (not simply continuous ones) are allowed as differentials. This extends the results of E. Wong and M. Zakai [Ann. Math. Stat. 36, 1560-1564 (1965; Zbl 0138.112), Z. Wahrscheinlichkeitstheor. Verw. Geb. 12, 87-97 (1969; Zbl 0185.444)], E. J. McShane [J. Multivariate Anal. 5, 121-177 (1975; Zbl 0323.60059)] and S. Nakao and Y. Yamato [Proc. int. Symp. on stochastic differential equations, Kyoto 1976, 283-297 (1978; Zbl 0443.60051)].
Reviewer: P.Kotelenez

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H20 Stochastic integral equations
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