Abstract
We consider jump-type stochastic differential equations with drift, diffusion, and jump terms. Logarithmic derivatives of densities for the solution process are studied, and Bismut–Elworthy–Li-type formulae are 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 Markov property of the process.
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Takeuchi, A. Bismut–Elworthy–Li-Type Formulae for Stochastic Differential Equations with Jumps. J Theor Probab 23, 576–604 (2010). https://doi.org/10.1007/s10959-010-0280-0
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DOI: https://doi.org/10.1007/s10959-010-0280-0