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By appealing to renewal theory we determine the equations that the mean exit time of a continuous-time random walk with drift satisfies both when the present coincides with a jump instant or when it does not. Particular attention is paid to the corrections ensuing from the non-Markovian nature of the process. We show that when drift and jumps have the same sign the relevant integral equations can be solved in closed form. The case when holding times have the classical Erlang distribution is considered in detail.
We consider random walk on dynamical percolation on the discrete torus $mathbb{Z}_n^d$. In previous work, mixing times of this process for $p<p_c(mathbb{Z}^d)$ were obtained in the annealed setting where one averages over the dynamical percolation en
In order to approximate the exit time of a one-dimensional diffusion process, we propose an algorithm based on a random walk. Such an algorithm so-called Walk on Moving Spheres was already introduced in the Brownian context. The aim is therefore to g
A novel version of the Continuous-Time Random Walk (CTRW) model with memory is developed. This memory means the dependence between arbitrary number of successive jumps of the process, while waiting times between jumps are considered as i.i.d. random
We consider the scaling behavior of the range and $p$-multiple range, that is the number of points visited and the number of points visited exactly $pgeq 1$ times, of simple random walk on ${mathbb Z}^d$, for dimensions $dgeq 2$, up to time of exit f
The simulation of exit times for diffusion processes is a challenging task since it concerns many applications in different fields like mathematical finance, neuroscience, reliability... The usual procedure is to use discretiza-tion schemes which unf