Corrected diffusion approximations for a perturbed random walk
翁新傑中研院經濟所 上午 10:00–12:00 鴻經館 107 室Abstract
Let {S_(θ,n), n ≥ 1} be a sequence of perturbed random walks indexed by θ, in thesense that the increments and drift depend on a small random noise. In this paper, we first consider a first passage time problem of S_(θ,n) crossing a constant boundary, and present a limiting distribution of the overshoot. Next we investigate the joint limiting distribution between the first passage time and the overshoot of the perturbed random walk. The asymptotic result for the boundary crossing problem is taken as θ↓0 simultaneously with the boundary goes to infinity. To this end, we present a uniform renewal theory for the perturbed random walk. In addition, we provide an interesting application. Numerical examples are also given.
keywords: Boundary crossing; uniform renewal theory; perturbed random walk; small random noise; overshoot; asymptotic independent.