The Bismut-Elworthy-Li type formulae for stochastic differential equations with jumps

Details The Bismut-Elworthy-Li type formulae for stochastic differential equations with jumps The Bismut-Elworthy-Li type formulae for stochastic differential equations with jumps

2010-02-06

arxiv.org/abs/1002.1384v1

Mathematics

Probability

29 pages, to appear in Journal of Theoretical Probability

Scientific paper

10.1007/s10959-010-0280-0

Consider jump-type stochastic differential equations with the drift, diffusion and jump terms. Logarithmic derivatives of densities for the solution process are studied, and the Bismut-Elworthy-Li type formulae can be obtained under the uniformly elliptic condition on the coefficients of the diffusion and jump terms. Our approach is based upon the Kolmogorov backward equation by making full use of the Markovian property of the process.

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