Moderate Deviation Principle for dynamical systems with small random perturbation
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arXiv
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| Format: | Preprint |
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2011
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| _version_ | 1866908955103461376 |
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| author | ma, Yutao Wang, Ran Wu, Liming |
| author_facet | ma, Yutao Wang, Ran Wu, Liming |
| contents | Consider the stochastic differential equation in $\rr^d$ dX^{\e}_t&=b(X^{\e}_t)dt+\sqrt{\e}σ(X^\e_t)dB_t X^{\e}_0&=x_0,\quad x_0\in\rr^d$ where $b:\rr^d\to\rr^d$ is $C^1$ such that $<x,b(x)> \leq C(1+|x|^2)$, $σ:\rr^d\to \MM(d\times n)$ is locally Lipschitzian with linear growth, and $B_t$ is a standard Brownian motion taking values in $\rr^n$. Freidlin-Wentzell's theorem gives the large deviation principle for $X^\e$ for small $\e$. In this paper we establish its moderate deviation principle. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1107_3432 |
| institution | arXiv |
| publishDate | 2011 |
| record_format | arxiv |
| spellingShingle | Moderate Deviation Principle for dynamical systems with small random perturbation ma, Yutao Wang, Ran Wu, Liming Probability 60F10, 60H10 Consider the stochastic differential equation in $\rr^d$ dX^{\e}_t&=b(X^{\e}_t)dt+\sqrt{\e}σ(X^\e_t)dB_t X^{\e}_0&=x_0,\quad x_0\in\rr^d$ where $b:\rr^d\to\rr^d$ is $C^1$ such that $<x,b(x)> \leq C(1+|x|^2)$, $σ:\rr^d\to \MM(d\times n)$ is locally Lipschitzian with linear growth, and $B_t$ is a standard Brownian motion taking values in $\rr^n$. Freidlin-Wentzell's theorem gives the large deviation principle for $X^\e$ for small $\e$. In this paper we establish its moderate deviation principle. |
| title | Moderate Deviation Principle for dynamical systems with small random perturbation |
| topic | Probability 60F10, 60H10 |
| url | https://arxiv.org/abs/1107.3432 |