Search results for "stochastic PDEs"

showing 2 items of 2 documents

Rough nonlocal diffusions

2019

We consider a nonlinear Fokker-Planck equation driven by a deterministic rough path which describes the conditional probability of a McKean-Vlasov diffusion with "common" noise. To study the equation we build a self-contained framework of non-linear rough integration theory which we use to study McKean-Vlasov equations perturbed by rough paths. We construct an appropriate notion of solution of the corresponding Fokker-Planck equation and prove well-posedness.

Statistics and ProbabilityRough pathApplied Mathematics60H05 60H15 60J60 35K55Probability (math.PR)Conditional probabilityMcKean-VlasovNoise (electronics)510Nonlinear systemMathematics - Analysis of PDEsRough paths60H05Modeling and Simulation35K5560H15FOS: MathematicsApplied mathematicsnon-local equationsDiffusion (business)stochastic PDEsMathematics - ProbabilityAnalysis of PDEs (math.AP)Mathematics
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Rough linear PDE's with discontinuous coefficients - existence of solutions via regularization by fractional Brownian motion

2020

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.

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
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