Bismut–Elworthy–Li-Type Formulae for Stochastic Differential Equations with Jumps

By Atsushi Takeuchi. 2010

46 citations recorded by the source corpus.

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.

Subfields: Finance, Mathematical Physics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/614490a044424bf25a35acedee98dee14bd10150

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2. Feng-Yu Wang
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Citations in the corpus

• Bismut formula for Lions derivative of distribution-path dependent SDEs (2020, methodology): “Due to their wide applications, the Bismut type formulas have been investigated for different models; see, for instance, [10, 25, 31, 32, 39, 41] for SDEs/SPDEs driven by jump processes, [16, 17, 24, 36, 35, 38, 40] for hypoelliptic diffusion semigroups, and [2, 14, 15] for SDEs with fractional nois”