2019
DOI: 10.1214/19-ejp352
|View full text |Cite
|
Sign up to set email alerts
|

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

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 simu… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
3
1
1

Citation Types

0
15
0

Year Published

2020
2020
2024
2024

Publication Types

Select...
3
2
2

Relationship

3
4

Authors

Journals

citations
Cited by 7 publications
(15 citation statements)
references
References 40 publications
0
15
0
Order By: Relevance
“…Indeed, it is enough to be able to compute the quantities E[1 {τ≥T } ] and E[1 {τ≥T } H T ] and plug them into the GD procedure. We refer to [3,10,16] for the exposition of unbiased simulation methods. Other methods to compute these quantities are PDE techniques, which we expect to be computationally heavier.…”
Section: Methodsmentioning
confidence: 99%
“…Indeed, it is enough to be able to compute the quantities E[1 {τ≥T } ] and E[1 {τ≥T } H T ] and plug them into the GD procedure. We refer to [3,10,16] for the exposition of unbiased simulation methods. Other methods to compute these quantities are PDE techniques, which we expect to be computationally heavier.…”
Section: Methodsmentioning
confidence: 99%
“…[9], and investigated from a numerical perspective by Andersson and Kohatsu-Higa [2]. We also mention the recent contribution of one the author with Kohatsu-Higa and Li [7] for IBP formulae for the marginal law of one-dimensional killed diffusion processes.…”
Section: Preliminaries: Assumptions Definition Of the Underlying Mark...mentioning
confidence: 99%
“…[9], Agarwal and Gobet [1] for multi-dimensional diffusion processes and in Frikha and al. [7] for one-dimensional killed processes. The major advantage of the aforementioned probabilistic formulae lies in the fact that an unbiased Monte Carlo simulation method directly stems from it.…”
Section: Introductionmentioning
confidence: 99%
See 2 more Smart Citations