Summary
The purpose of this paper is to develop a stochastic calculus of variations for R n-valuedstrong Markov processes with jumps x t ,which is the analogous of the Malliavin calculus of variations on diffusions. An integration by parts formula is established on a non Gaussian infinite dimensional probability space, in order to prove regularity of the probability law on R nof x t ,for fixed time t. Diffusions with jumps are also considered. The connection between the calculus of variations and the representations of martingales for jump process is exhibited.
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Bismut, JM. Calcul des variations stochastique et processus de sauts. Z. Wahrscheinlichkeitstheorie verw Gebiete 63, 147–235 (1983). https://doi.org/10.1007/BF00538963
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DOI: https://doi.org/10.1007/BF00538963