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2019 Integration by parts formula for killed processes: a point of view from approximation theory
Noufel Frikha, Arturo Kohatsu-Higa, Libo Li
Electron. J. Probab. 24(none): 1-44 (2019). DOI: 10.1214/19-EJP352

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.

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Noufel Frikha. Arturo Kohatsu-Higa. Libo Li. "Integration by parts formula for killed processes: a point of view from approximation theory." Electron. J. Probab. 24 1 - 44, 2019. https://doi.org/10.1214/19-EJP352

Information

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

zbMATH: 07107402
MathSciNet: MR4017113
Digital Object Identifier: 10.1214/19-EJP352

Subjects:
Primary: 60H07, 60H20, 60H30, 65C05, 65C30

JOURNAL ARTICLE
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Vol.24 • 2019
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