Moderate deviations for rough differential equations
Yuzuru Inahama, Yong Xu, Xiaoyu Yang
TL;DR
This paper establishes a moderate deviation principle for rough differential equations driven by scaled fractional Brownian rough paths with Hurst parameter between 1/4 and 1/2, highlighting the behavior of solutions under small noise.
Contribution
It introduces a moderate deviation principle for rough differential equations driven by fractional Brownian rough paths with Hurst parameter in (1/4, 1/2).
Findings
Proves a moderate deviation principle for the specified rough differential equations.
Extends understanding of small noise asymptotics in rough path settings.
Provides theoretical foundation for analyzing fluctuations in fractional Brownian-driven systems.
Abstract
Small noise problems are quite important for all types of stochastic differential equations. In this paper we focus on rough differential equations driven by scaled fractional Brownian rough path with Hurst parameter H between 1/4 and 1/2. We prove a moderate deviation principle for this equation as the scale parameter tends to zero.
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Taxonomy
TopicsStochastic processes and financial applications · Stochastic processes and statistical mechanics · Financial Risk and Volatility Modeling