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On degenerate linear stochastic evolution equations driven by jump processes

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  • Leahy, James-Michael
  • Mikulevičius, Remigijus

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.

Suggested Citation

  • Leahy, James-Michael & Mikulevičius, Remigijus, 2015. "On degenerate linear stochastic evolution equations driven by jump processes," Stochastic Processes and their Applications, Elsevier, vol. 125(10), pages 3748-3784.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:10:p:3748-3784
    DOI: 10.1016/j.spa.2015.05.007
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    References listed on IDEAS

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    1. Peszat, S. & Zabczyk, J., 2013. "Time regularity of solutions to linear equations with Lévy noise in infinite dimensions," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 719-751.
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    Cited by:

    1. Qiu, Jinniao, 2020. "L2-theory of linear degenerate SPDEs and Lp (p>0) estimates for the uniform norm of weak solutions," Stochastic Processes and their Applications, Elsevier, vol. 130(3), pages 1206-1225.

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    More about this item

    Keywords

    Systems of stochastic integro-differential equations; L2 theory; Degenerate stochastic parabolic PDEs; Levy processes;
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    JEL classification:

    • L2 - Industrial Organization - - Firm Objectives, Organization, and Behavior

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