The risk-neutral process is modeled by a four parameter self-similar process of independent increments with a self-decomposable law for its unit time distribution. Six different processes in this general class are theoretically formulated and empirically investigated. We show that all six models...

In this work a three parameter stochastic process, termed the Gamma-Ornstein–Uhlenbeck process, has been implemented to analyze geophysical data. Such non-Gaussian Ornstein–Uhlenbeck processes offer the possibility of capturing important distributional deviations from Gaussianity and make...

The existence of strong and weak càdlàg versions of a solution to a linear equation in a Hilbert space H, driven by a Lévy process taking values in a Hilbert space U↩H is established. The so-called cylindrical càdlàg property is investigated as well. A special emphasis is put on infinite...

In this paper, we obtain the moderate deviation principle for a sequence of Brownian motions defined on the unit sphere in Rd by using the cumulant method introduced by  Puhalskii (1994b) and generalize it to Ornstein–Uhlenbeck processes taking values on the unit sphere in Rd.

We use a Stochastic Differential Equation satisfied by Brownian motion taking values in the unit sphere Sn−1⊂Rn and we obtain a Central Limit Theorem for a sequence of such Brownian motions. We also generalize the results to the case of the n-dimensional Ornstein–Uhlenbeck processes.

A statistical inference for ruin probability from a certain discrete sample of the surplus is discussed under a spectrally negative Lévy insurance risk. We consider the Laguerre series expansion of ruin probability, and provide an estimator for any of its partial sums by computing the...

We consider the model selection problem for ergodic diffusion processes based on sampled data. The adaptive estimators for parameters of drift and diffusion coefficients are used in order to construct Akaike’s information criterion (AIC) type model selection statistics. Asymptotic properties...

For a continuous-time Markov process, occasionally, only discrete-time observations are available. For a simple sample of homogeneous Markov jump processes with an absorbing state, observed each on a stochastic grid of time points, we establish asymptotic normality of the maximum likelihood...

We consider parametric hypotheses testing for multidimensional ergodic diffusion processes observed at discrete time. We propose a family of test statistics related to the so called ϕ-divergence measures. It is proved that the test statistics in this family are all asymptotically distribution...

We study the problem of parameter estimation for discretely observed stochastic processes driven by additive small Lévy noises. We do not impose any moment condition on the driving Lévy process. Under certain regularity conditions on the drift function, we obtain consistency and rate of...