Large deviation for small noise path-dependent stochastic differential equations

Liu Xiangdong; Hong Shaopeng

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arXiv · 2303.17840

Large deviation for small noise path-dependent stochastic differential equations

Liu Xiangdong·Hong Shaopeng

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Abstract

In this paper, we study the asymptotic behavior of randomly perturbed path-dependent stochastic differential equations with small parameter $\vartheta_{\varepsilon}$, when $\varepsilon \rightarrow 0$, $\vartheta_\varepsilon$ goes to $0$. When $\varepsilon \rightarrow 0$, we establish large deviation principle. The proof of the results relies on the weak convergence approach. As an application, we establish the large deviation for functionals of path-dependent SDEs in small time intervals.

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Liu Xiangdong, Hong Shaopeng. 2023-03-31. Large deviation for small noise path-dependent stochastic differential equations. https://arxiv.org/abs/2303.17840

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