Harnack Inequalities for McKean-Vlasov SDEs Driven by Subordinate Brownian Motions
Chang-Song Deng, Xing Huang
TL;DR
This paper establishes existence, uniqueness, and Harnack inequalities for McKean-Vlasov SDEs driven by subordinate Brownian motions, advancing understanding of these stochastic systems with Lévy process influences.
Contribution
It introduces new methods to prove Harnack inequalities for McKean-Vlasov SDEs driven by subordinate Brownian motions, extending previous results to Lévy process-driven equations.
Findings
Proved existence and uniqueness of solutions.
Established Harnack inequalities for the equations.
Developed an approximation and coupling method for analysis.
Abstract
The existence and uniqueness are established for McKean-Vlasov SDEs driven by L\'{e}vy processes. By using an approximation technique and coupling by change of measures, Harnack inequalities are investigated for McKean-Vlasov SDEs driven by subordinate Brownian motions.
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Taxonomy
TopicsFinancial Markets and Investment Strategies · Stochastic processes and financial applications · Market Dynamics and Volatility