Sharp error terms and neccessary conditions for exponential hitting times in mixing processes

Statistics and Error Terms of Occurrence Times in Mixing 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

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

Mixing and hitting times for finite Markov chains

Let 0 < α < 1/2. We show that that the mixing time of a continuous-time Markov chain on a finite state space is about as large as the largest expected hitting time of a subset of the state space with stationary measure ≥ α. Suitably modified results hold in discrete time and/or without the reversibility assumption. The key technical tool in the proof is the construction of random set A such tha...