Integration by Parts formula for SPDEs with Multiplicative Noise and its Applications
Xing Huang, Shao-Qin Zhang, Li-Xia Liu
TL;DR
This paper develops an integration by parts formula for SPDEs with multiplicative noise using Malliavin calculus and provides heat kernel density estimates in finite dimensions.
Contribution
It introduces a Driver-type integration by parts formula for the semigroup of SPDEs with multiplicative noise, expanding analytical tools in this area.
Findings
Established a Malliavin calculus-based integration by parts formula for SPDEs.
Derived heat kernel density estimates in finite-dimensional cases.
Abstract
By using the Malliavin calculus, the Driver-type integration by parts formula is established for the semigroup associated to to SPDEs with Multiplicative Noise. Moreover, estimates on the density of heat kernel w.r.t. Lebesgue measure are obtained in finite dimension case.
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Taxonomy
TopicsStochastic processes and financial applications · Advanced Mathematical Modeling in Engineering · Stability and Controllability of Differential Equations