Fractional Poisson processes, a rapidly growing area of non-Markovian stochastic processes, are useful in statistics to describe data from counting processes when waiting times are not exponentially distributed. We show that the fractional Kolmogorov–Feller equations for the probabilities at...

We study backward stochastic differential equations (BSDEs) for time-changed Lévy noises when the time-change is independent of the Lévy process. We prove existence and uniqueness of the solution and we obtain an explicit formula for linear BSDEs and a comparison principle. BSDEs naturally...

Tests for parametric nonhomogeneous and homogeneous Markov processes are given. Asymptotic distribution of test statistics is investigated. Tests for various well-known models are discussed as examples. Copyright Springer-Verlag Berlin Heidelberg 2014

We consider the optimal reinsurance and investment problem in an unobservable Markov-modulated compound Poisson risk model, where the intensity and jump size distribution are not known but have to be inferred from the observations of claim arrivals. Using a recently developed result from...

Interval-censored survival data are often recorded in medical practice. Although some methods have been developed for analyzing such data, issues still remain in terms of efficiency and accuracy in estimation. In addition, interval-censored data with spatial correlation are not unusual but less...