Convergence of hitting times for jump-diffusion processes

Hitting times for Gaussian processes

We establish a general formula for the Laplace transform of the hitting times of a Gaussian process. Some consequences are derived, and in particular cases like the fractional Brownian motion are discussed. AMS Subject Classification: 60H05, 60H07

Double-barrier first-passage times of jump-diffusion processes

Required in a wide range of applications in, e.g., finance, engineering, and physics, first-passage time problems have attracted considerable interest over the past decades. Since analytical solutions often do not exist, one strand of research focuses on fast and accurate numerical techniques. In this paper, we present an efficient and unbiased Monte-Carlo simulation to obtain double-barrier fi...

Central Limit Theorem for Hitting times of Functionals of Markov Jump Processes

A sample of i.i.d. continuous time Markov chains being defined, the sum over each component of a real function of the state is considered. For this functional, a central limit theorem for the first hitting time of a prescribed level is proved. The result extends the classical central limit theorem for order statistics. Various reliability models are presented as examples of applications. Mathem...

Hitting times for Multiplicative Growth-collapse Processes

We consider a stochastic process (Xt)t≥0 that grows linearly in time and experiences collapses at times governed by a Poisson process with rate λ. The collapses are modeled by multiplying the process level by a random variable supported on [0, 1). For the hitting time defined as τy = inf{t > 0|Xt = y} we derive power series for the Laplace transform and all moments. We further discuss the asymp...

Probability HITTING TIMES FOR GAUSSIAN PROCESSES