论文标题
具有分数布朗噪声的随机动力学系统的大偏差原理
Large deviation principles for stochastic dynamical systems with a fractional Brownian noise
论文作者
论文摘要
我们研究了小噪声，用于随机微分方程的较小偏差渐近方程，其乘积噪声为分数布朗运动$ b^h $带有hurst参数$ h> \ frac12 $。随机微分方程的溶液在适当条件下在系数的适当条件下将其定义。大偏差原理证明中的成分，其中包括分数布朗动作的非负功能的变异表示，以及用于LDP的一般条件，用于分数布朗尼运动的功能集合，具有比此处考虑的模型更广泛的适用性。
We study small noise large deviation asymptotics for stochastic differential equations with a multiplicative noise given as a fractional Brownian motion $B^H$ with Hurst parameter $H>\frac12$. The solutions of the stochastic differential equations are defined pathwise under appropriate conditions on the coefficients. The ingredients in the proof of the large deviation principle, which include a variational representation for nonnegative functionals of fractional Brownian motions and a general sufficient condition for a LDP for a collection of functionals of a fractional Brownian motions, have a broader applicability than the model considered here.
