Varadhan Estimates for rough differential equations driven by fractional Brownian motions
Fabrice Baudoin, Cheng Ouyang, Xuejing Zhang
TL;DR
This paper establishes Varadhan's small time estimates for the density of solutions to rough differential equations driven by fractional Brownian motion with Hurst parameter greater than 1/4, under Hormander's conditions.
Contribution
It extends Varadhan's estimates to rough differential equations driven by fractional Brownian motion with H>1/4, a novel setting in stochastic analysis.
Findings
Varadhan's estimates are proved for fractional Brownian motion-driven equations.
Results apply under Hormander's type conditions.
The work advances understanding of densities in rough stochastic systems.
Abstract
In this work we study rough differential equations driven by a fractional Brownian motion with Hurst parameter H>1/4 and establish Varadhan's small time estimates for the density of solutions of such equations under Hormander's type conditions.
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Taxonomy
TopicsStochastic processes and financial applications · Mathematical Dynamics and Fractals · Advanced Mathematical Modeling in Engineering