Approximation of the Exit Probability of a Stable Markov Modulated Constrained Random Walk

Fatma Başoğlu Kabran, Ali Devin Sezer

Let $X$ be the constrained random walk on ${\mathbb{Z}}_{+}^2$ having increments $(1,0)$, $(-1,1)$, $(0,-1)$ with jump probabilities $\lambda (M_k)$, ${\mu }_1(M_k)$, and ${\mu }_2(M_k)$ where $M$ is…