Recurrence relations for generalized hitting times for semi-Markov 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

Interactive Generalized Semi-Markov Processes

We have previously introduced Generalized Semi-Markovian Process Algebra (GSMPA), a process algebra based on ST semantics which is capable of expressing durational actions, where durations are expressed by general probability distributions. In this paper we introduce the calculus of Interactive Generalized Semi-Markov Processes (IGSMP), a variant of GSMPA where synchronizable actions are restri...

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

Recurrence Relations for Quotient Moment of Generalized Pareto Distribution Based on Generalized Order Statistics and Characterization

Generalized Pareto distribution play an important role in reliability, extreme value theory, and other branches of applied probability and statistics. This family of distributions includes exponential distribution, Pareto distribution, and Power distribution. In this paper, we established exact expressions and recurrence relations satisfied by the quotient moments of generalized order statistic...