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2018 Approximating diffusion reflections at elastic boundaries
Dirk Becherer, Todor Bilarev, Peter Frentrup
Electron. Commun. Probab. 23: 1-12 (2018). DOI: 10.1214/18-ECP141

Abstract

We show a probabilistic functional limit result for one-dimensional diffusion processes that are reflected at an elastic boundary which is a function of the reflection local time. Such processes are constructed as limits of a sequence of diffusions which are discretely reflected by small jumps at an elastic boundary, with reflection local times being approximated by $\varepsilon $-step processes. The construction yields the Laplace transform of the inverse local time for reflection. Processes and approximations of this type play a role in finite fuel problems of singular stochastic control.

Citation

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Dirk Becherer. Todor Bilarev. Peter Frentrup. "Approximating diffusion reflections at elastic boundaries." Electron. Commun. Probab. 23 1 - 12, 2018. https://doi.org/10.1214/18-ECP141

Information

Received: 25 September 2017; Accepted: 30 May 2018; Published: 2018
First available in Project Euclid: 21 June 2018

zbMATH: 1394.60023
MathSciNet: MR3820130
Digital Object Identifier: 10.1214/18-ECP141

Subjects:
Primary: 60F17, 60J50, 60J55, 60J60, 65C30

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