0000000000887019

AUTHOR

Michele Coghi

showing 2 related works from this author

Rough McKean-Vlasov dynamics for robust ensemble Kalman filtering

2021

Motivated by the challenge of incorporating data into misspecified and multiscale dynamical models, we study a McKean-Vlasov equation that contains the data stream as a common driving rough path. This setting allows us to prove well-posedness as well as continuity with respect to the driver in an appropriate rough-path topology. The latter property is key in our subsequent development of a robust data assimilation methodology: We establish propagation of chaos for the associated interacting particle system, which in turn is suggestive of a numerical scheme that can be viewed as an extension of the ensemble Kalman filter to a rough-path framework. Finally, we discuss a data-driven method bas…

60L20 60L90 60H10 60F99 65C35 62M05Probability (math.PR)FOS: MathematicsMathematics - Statistics TheoryMathematics - Numerical AnalysisNumerical Analysis (math.NA)Statistics Theory (math.ST)Mathematics - Probability
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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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