Electronic Journal of Probability

Integration by parts formula for killed processes: a point of view from approximation theory

Noufel Frikha, Arturo Kohatsu-Higa, and Libo Li

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Abstract

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.

Article information

Source
Electron. J. Probab., Volume 24 (2019), paper no. 95, 44 pp.

Dates
Received: 28 December 2018
Accepted: 6 August 2019
First available in Project Euclid: 18 September 2019

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1568793788

Digital Object Identifier
doi:10.1214/19-EJP352

Subjects
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

Keywords
expansions stochastic differential equations killed process integration by parts Monte Carlo simulation

Rights
Creative Commons Attribution 4.0 International License.

Citation

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


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