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L2-theory of linear degenerate SPDEs and Lp (p>0) estimates for the uniform norm of weak solutions

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  • Qiu, Jinniao

Abstract

In this paper, we are concerned with possibly degenerate stochastic partial differential equations (SPDEs). An L2-theory is introduced, from which we derive a Hörmander-type theorem with an analytical approach. With the method of De Giorgi iteration, we obtain the maximum principle which states the Lp (p>0) estimates for the time-space uniform norm of weak solutions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:3:p:1206-1225
    DOI: 10.1016/j.spa.2019.04.011
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    References listed on IDEAS

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    1. 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.
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