The Onsager-Machlup functional associated with additive fractional noise

Yohaï Maayan

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arXiv · 1705.08976

The Onsager-Machlup functional associated with additive fractional noise

Yohaï Maayan

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Abstract

We consider the solution of a stochastic differential equation with additive multidimensional fractional noise. In the case $\frac14<H<\frac12$, we compute the Onsager-Machlup functional (with respect to the driving fractional Brownian motion) for the supremum norm and the H\"older norms with exponent $\alpha \in \left(0,H-\frac14\right)$ for any element of the Cameron-Martin space $\mathcal H_H$, extending a previous result of Moret and Nualart. In the more general case $H<\frac12$ and $\alpha \in \left(0,H\right)$, we formulate a condition on $h\in\mathcal H_H$ under which the computation of the Onsager-Machlup functional $J\left(h\right)$ follows.

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Yohaï Maayan. 2017-05-24. The Onsager-Machlup functional associated with additive fractional noise. https://arxiv.org/abs/1705.08976

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