Hörmander-Type Theorem for Itô Processes and Related Backward SPDEs

Abstract

A Hörmander-type theorem is established for Itô processes and related backward stochastic partial differential equations (BSPDEs). A short self-contained proof is also provided for the $L^2$-theory of linear, possibly degenerate BSPDEs, in which new gradient estimates are obtained.

15 pages

References in corpus (2)

• On the Cauchy problem for backward stochastic partial differential equations in Hölder spaces
• Hörmander's theorem for stochastic partial differential equations

Cited by in corpus (1)

• Viscosity Solutions of Stochastic Hamilton-Jacobi-Bellman Equations