Bismut Formula for Intrinsic/Lions Derivatives of Distribution Dependent SDEs with Singular Coefficients
Xing Huang, Yulin Song, Feng-Yu Wang
TL;DR
This paper develops a Bismut formula for intrinsic and Lions derivatives of distribution dependent SDEs with singular coefficients, extending classical results to more complex, irregular systems using advanced calculus techniques.
Contribution
It introduces a novel Bismut formula for derivatives of distribution dependent SDEs with singular drifts, utilizing Zvonkin's transforms and Malliavin calculus.
Findings
Derived Bismut formula for singular distribution dependent SDEs
Generalized classical Bismut formulas to irregular systems
Extended applicability to a broader class of SDEs
Abstract
By using distribution dependent Zvonkin's transforms and Malliavin calculus, the Bismut type formula is derived for the intrinisc/Lions derivatives of distribution dependent SDEs with singular drifts, which generalizes the corresponding results derived for classical SDEs and regular distribution dependent SDEs.
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Taxonomy
TopicsStochastic processes and financial applications · Monetary Policy and Economic Impact