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Upper bounds for the maximum of a random walk with negative drift
Limit theorems random walks renewal theorem
2011/9/21
Abstract: Consider a random walk $S_n=\sum_{i=0}^n X_i$ with negative drift. This paper deals with upper bounds for the maximum $M=\max_{n\ge 1}S_n$ of this random walk in different settings of power ...
Fractional Laplacian with singular drift
fractional Laplacian gradient perturbations singular drift
2011/9/13
Abstract: For $\alpha \in (1,2)$ we consider the equation $\partial_t u = \Delta^{\alpha/2} u - r b \cdot \nabla u$, where $b$ is a divergence free singular vector field not necessarily belonging to t...
Stationary distributions for jump processes with inert drift
Stationary distributions jump processes inert drift
2010/12/6
We analyze jump processes Z with “inert drift” determined by a “memory”process S. The state space of (Z, S) is the Cartesian product of the unit circle and the real line. We prove that the stationary ...