Extrinsic derivatives for SDEs and SPDEs with distribution dependent noise
Xiaochen Ma, Panpan Ren
TL;DR
This paper develops a Bismut type formula for the extrinsic derivative of McKean-Vlasov SDEs and extends it to certain distribution dependent SPDEs, advancing the analysis of stochastic systems with distribution-dependent noise.
Contribution
It introduces a novel Bismut formula for extrinsic derivatives in McKean-Vlasov SDEs and extends this to a class of distribution dependent SPDEs, filling a gap in stochastic analysis.
Findings
Established a Bismut type formula for McKean-Vlasov SDEs with distribution dependent noise.
Extended the formula to a class of distribution dependent SPDEs.
Provides new tools for analyzing regularities of stochastic systems with distribution-dependent noise.
Abstract
The Bismut formula is a crucial tool characterizing regularities of stochastic systems, and has been extensively studied for various models. However it is not yet available for SDEs with distribution dependent noise. In this paper, we first establish a Bismut type formula for the extrinsic derivative of McKean-Vlasov SDEs driven by distribution dependent noise, then make an extension to a class of distribution dependent SPDEs.
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Taxonomy
TopicsStochastic processes and financial applications · Risk and Portfolio Optimization · Economic theories and models