6533b85efe1ef96bd12bfe7b

RESEARCH PRODUCT

Rough linear PDE's with discontinuous coefficients - existence of solutions via regularization by fractional Brownian motion

Torstein Nilssen

subject

Statistics and ProbabilityFractional Brownian motion010102 general mathematicsMathematical analysisProbability (math.PR)fractional Brownian motionlocal times01 natural sciencesRegularization (mathematics)VDP::Matematikk og Naturvitenskap: 400::Matematikk: 410010104 statistics & probabilityDeterministic equation60H05FOS: Mathematics60H1560J5560H1060G220101 mathematicsStatistics Probability and Uncertaintystochastic PDEsrough pathsregularization by noiseMathematics - ProbabilityMathematics

description

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.

yearjournalcountryeditionlanguage
2020-01-01
http://arxiv.org/abs/1509.01154