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

Jinniao Qiu

Stochastic Processes and their Applications, 2020, vol. 130, issue 3, 1206-1225

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.

Keywords: Stochastic partial differential equation; L2-theory; Hörmander theorem; Maximum principle; De Giorgi iteration (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:130:y:2020:i:3:p:1206-1225

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DOI: 10.1016/j.spa.2019.04.011

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