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

2015/03/20 by Jinniao Qiu, Qiu, Jinniao
Economics, Econometrics and Finance · Engineering · Mathematics · #35D30 #35R60 #60H15 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1503.06162

openalex publication_date 2015/03/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

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

Citations

• Hörmander-Type Theorem for Itô Processes and Related Backward SPDEs
• Hörmander's theorem for stochastic partial differential equations
• On Degenerate Linear Stochastic Evolution Equations Driven by Jump Processes

Related

• Stochastic Partial Differential Equations with Unbounded and Degenerate Coefficients
• An L²-theory on SPDE driven by Lévy processes
• Maximum principle for non-uniformly parabolic equations and applications
• On weak uniqueness for some degenerate SDEs by global L^p estimates
• An L^p-theory of non-divergence form SPDEs driven by Lévy processes