Stochastic calculus for Gaussian processes and application to hitting times

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

Probability HITTING TIMES FOR GAUSSIAN PROCESSES

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...

Stochastic Calculus for Dirichlet Processes

Using time-reversal, we introduce the stochastic integration for zero-energy additive functionals of symmetric Markov processes, which extends an early work of S. Nakao. Various properties of such stochastic integrals are discussed and an Itô formula for Dirichlet processes is obtained. AMS 2000 Mathematics Subject Classification: Primary 31C25; Secondary 60J57, 60J55, 60H05.

Asymptotics for Hitting Times

In this paper we characterize possible asymptotics for hitting times in aperiodic ergodic dynamical systems: asymptotics are proved to be the distribution functions of subprobability measures on the line belonging to the functional class (A) F = F is continuous and concave; F (t) ≤ t for t ≥ 0.. Note that all possible asymptotics are absolutely continuous.