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2020 Rough linear PDE’s with discontinuous coefficients – existence of solutions via regularization by fractional Brownian motion
Torstein Nilssen
Electron. J. Probab. 25: 1-33 (2020). DOI: 10.1214/20-EJP437

Abstract

We consider two related linear PDE’s perturbed by a fractional Brownian motion. We allow the drift to be discontinuous, in which case the corresponding deterministic equation is ill-posed. However, the noise will be shown to have a regularizing effect on the equations in the sense that we can prove existence of solutions for almost all paths of the fractional Brownian motion.

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Torstein Nilssen. "Rough linear PDE’s with discontinuous coefficients – existence of solutions via regularization by fractional Brownian motion." Electron. J. Probab. 25 1 - 33, 2020. https://doi.org/10.1214/20-EJP437

Information

Received: 25 June 2018; Accepted: 28 February 2020; Published: 2020
First available in Project Euclid: 20 March 2020

zbMATH: 1441.60048
MathSciNet: MR4089784
Digital Object Identifier: 10.1214/20-EJP437

Subjects:
Primary: 60G22, 60H05, 60H10, 60H15, 60J55

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