On Degenerate Linear Stochastic Evolution Equations Driven by Jump Processes

2014/06/17 by James-Michael Leahy, Leahy, James-Michael, R. Mikulevíčius +1 · 1 citation
Computer Science · Economics, Econometrics and Finance · Engineering · #35K65 #45K05 #60H15 #60H20 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1406.4541

openalex publication_date 2014/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the existence and uniqueness of solutions of degenerate linear stochastic evolution equations driven by jump processes in a Hilbert scale using the variational framework of stochastic evolution equations and the method of vanishing viscosity. As an application of this result, we derive the existence and uniqueness of solutions of degenerate parabolic linear stochastic integro-differential equations (SIDEs) in the Sobolev scale. The SIDEs that we consider arise in the theory of non-linear filtering as the equations governing the conditional density of a degenerate jump-diffusion signal given a jump-diffusion observation, possibly with correlated noise.

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• L²-Theory of Linear Degenerate SPDEs and L^p (p>0) Estimates for the Uniform Norm of Weak Solutions

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