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April, 1986 The Malliavin Calculus for Pure Jump Processes and Applications to Local Time
R. F. Bass, M. Cranston
Ann. Probab. 14(2): 490-532 (April, 1986). DOI: 10.1214/aop/1176992528


A Malliavin calculus is developed whose scope includes point processes, pure jump Markov processes, and purely discontinuous martingales. An integration by parts formula for functionals of Poisson point processes is proved. This is used to develop a criterion for pure jump Markov processes to have a density in $L^p$. The integration by parts formula is then used to give conditions for a purely discontinuous martingale to have a jointly continuous local time $L^x_t$ that is an occupation time density with respect to Lebesgue measure.


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R. F. Bass. M. Cranston. "The Malliavin Calculus for Pure Jump Processes and Applications to Local Time." Ann. Probab. 14 (2) 490 - 532, April, 1986.


Published: April, 1986
First available in Project Euclid: 19 April 2007

zbMATH: 0595.60044
MathSciNet: MR832021
Digital Object Identifier: 10.1214/aop/1176992528

Primary: 60G44
Secondary: 60G57 , 60J35 , 60J55

Keywords: Local times , Malliavin calculus , Martingales , Point processes , pure jump Markov processes , Stochastic differential equations

Rights: Copyright © 1986 Institute of Mathematical Statistics


Vol.14 • No. 2 • April, 1986
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