Book chapter
Large Deviation Principles for Functionals of Fractional Brownian Motions
Frontiers of Statistics and Data Science, pp 101-131
01 Jun 2025
Abstract
We study small noise large deviation asymptotics for functionals of fractional Brownian motions. A general sufficient condition for an LDP, formulated in terms of weak convergence properties of certain controlled analogs of the original functionals, is presented. As an application, we prove large deviation principles for a class of stochastic differential equations with a multiplicative noise given as a fractional Brownian motion BH\documentclass[12pt]{minimal}
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\begin{document}$$B^H$$\end{document} with Hurst parameter H>12\documentclass[12pt]{minimal}
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\begin{document}$$H>\frac{1}{2}$$\end{document}. The methods presented have broader applicability than the model considered here, for example, to systems driven by more general Gaussian noises and infinite dimensional stochastic dynamical systems with fractional Gaussian noises.
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Details
- Title
- Large Deviation Principles for Functionals of Fractional Brownian Motions
- Creators
- Amarjit BudhirajaXiaoming Song
- Contributors
- Subhashis Ghosal (Editor)Anindya Roy (Editor)
- Publication Details
- Frontiers of Statistics and Data Science, pp 101-131
- Series
- IISA Series on Statistics and Data Science
- Publisher
- Springer Nature Singapore; Singapore
- Resource Type
- Book chapter
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991022054406204721