Smooth densities for SDEs driven by subordinated Brownian motion with Markovian switching
Xiaobin Sun, Yingchao Xie
TL;DR
This paper investigates the smoothness of probability densities for solutions to stochastic differential equations driven by subordinate Brownian motion with Markovian switching, using Malliavin calculus under Hörmander-type conditions.
Contribution
It introduces a novel analysis of SDEs with subordinate Brownian motion and Markovian switching, establishing conditions for smooth densities via Malliavin calculus.
Findings
Established smoothness of densities under Hörmander conditions
Applied Malliavin calculus to SDEs with subordinate Brownian motion
Extended analysis to include Markovian switching mechanisms
Abstract
In this paper we consider a class of stochastic differential equations driven by subordinate Brownian motion with Markovian switching. We use Malliavin calculus to study the smoothness of the density for the solution under uniform H\"ormander's type condition.
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Taxonomy
TopicsStochastic processes and financial applications