×

Integration by parts for the single jump process. (English) Zbl 0749.60044

For a general jump process a small perturbation is compensated by changing the measure, so that differentiating gives a new integration by parts formula. Consequently, this also gives a new martingale representation.

MSC:

60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
60H05 Stochastic integrals
60G44 Martingales with continuous parameter
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Bismut, J. M., Martingales, the Malliavin calculus and hypoellipticity under general Hörmander’s conditions, Z. Wahrsch. Verw. Gebiete, 56 (1981) · Zbl 0445.60049
[2] Elliott, R. J., Stochastic calculus and applications, Applications of Mathematics No. 18 (1982), Springer: Springer Berlin—Heidelberg—New York · Zbl 0503.60062
[3] Norris, J. R., Integration by parts for jump processes, Séminaire de Probabilités XXII. Lecture Notes in Math. No. 1321 (1988), Springer: Springer Berlin · Zbl 0649.60080
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.