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Simulating the Maximum of a Random Walk
Random walk Single-server queue Simulation Stationary distribution
2015/7/8
In this paper, we show how to exactly sample from the distribution of the maximum of a random walk with negative drift. We also explore related variance reduction methods.
Diffusion Approximations for the Maximum of a Perturbed Random Walk
Perturbed random walk diffusion approximation light-tailed distributi
2015/7/6
Considera random walk S=(Sn:n≥O) that is "perturbed" by a stationary sequence (ξn:n≥O) to produce the process S=(Sn+ξn:n≥O). In this paper, we are concerned with developing limit theorems and approxim...
Tail Asymptotics for the Maximum of Perturbed Random Walk
Perturbed random walk Cramér–Lundberg approximation coupling heavy tails
2015/7/6
Consider a random walk S = (Sn:n≥0) that is “perturbed” by a stationary sequence (ξn:n≥0) to produce the process (Sn+ξn:n≥0). This paper is concerned with computing the distribution of the all-time ma...
Complete Corrected Diffusion Approximations for the Maximum of a Random Walk
Corrected diffusion approximations random walks ladder heights single-server queue
2015/7/6
Consider a random walk (Sn: n ≥ 0) with drift −μ and S0= 0. Assuming that the increments have exponential moments, negative mean, and are strongly nonlattice, we provide a complete asymptotic ex...