Electronic Journal of Probability
- Electron. J. Probab.
- Volume 24 (2019), paper no. 95, 44 pp.
Integration by parts formula for killed processes: a point of view from approximation theory
In this paper, we establish a probabilistic representation for two integration by parts formulas, one being of Bismut-Elworthy-Li’s type, for the marginal law of a one-dimensional diffusion process killed at a given level. These formulas are established by combining a Markovian perturbation argument with a tailor-made Malliavin calculus for the underlying Markov chain structure involved in the probabilistic representation of the original marginal law. Among other applications, an unbiased Monte Carlo path simulation method for both integration by parts formula stems from the previous probabilistic representations.
Electron. J. Probab., Volume 24 (2019), paper no. 95, 44 pp.
Received: 28 December 2018
Accepted: 6 August 2019
First available in Project Euclid: 18 September 2019
Permanent link to this document
Digital Object Identifier
Primary: 60H20: Stochastic integral equations 60H07: Stochastic calculus of variations and the Malliavin calculus 60H30: Applications of stochastic analysis (to PDE, etc.) 65C05: Monte Carlo methods 65C30: Stochastic differential and integral equations
Frikha, Noufel; Kohatsu-Higa, Arturo; Li, Libo. Integration by parts formula for killed processes: a point of view from approximation theory. Electron. J. Probab. 24 (2019), paper no. 95, 44 pp. doi:10.1214/19-EJP352. https://projecteuclid.org/euclid.ejp/1568793788