An i.i.d. process is considered on a compact metric space . Its marginal distribution [pi] is unknown, but is assumed to lie in a moment class of the form, where {fi} are real-valued, continuous functions on , and {ci} are constants. The following conclusions are obtained: (i) For any...

We consider a Markovian regime switching insurance risk model (also called Markov-modulated risk model). The closed form solutions for the joint distribution of surplus before and after ruin when the initial surplus is zero or when the claim size distributions are phase-type distributed are...

In this paper, we propose some algorithms for the simulation of the distribution of certain diffusions conditioned on a terminal point. We prove that the conditional distribution is absolutely continuous with respect to the distribution of another diffusion which is easy for simulation, and the...

The martingale problem for superprocesses with parameters ([xi],[Phi],k) is studied where may not be absolutely continuous with respect to the Lebesgue measure. This requires a generalization of the concept of martingale problem: we show that for any process X which partially solves the...

Ultraslow diffusion is a physical model in which a plume of diffusing particles spreads at a logarithmic rate. Governing partial differential equations for ultraslow diffusion involve fractional time derivatives whose order is distributed over the interval from zero to one. This paper develops...

We consider a stochastic delay differential equation driven by a general Lévy process. Both the drift and the noise term may depend on the past, but only the drift term is assumed to be linear. We show that the segment process is eventually Feller, but in general not eventually strong Feller on...

This paper is devoted to analyzing several properties of the bifractional Brownian motion introduced by Houdré and Villa. This process is a self-similar Gaussian process depending on two parameters H and K and it constitutes a natural generalization of fractional Brownian motion (which is...

Given a smooth -valued diffusion starting at point x, we study how fast the Euler scheme with time step 1/n converges in law to the random variable . To be precise, we look for the class of test functions f for which the approximate expectation converges with speed 1/n to . When f is smooth with...

The multifractional Brownian motion (MBM) processes are locally self-similar Gaussian processes. They extend the classical fractional Brownian motion processes by allowing their self-similarity parameter H[set membership, variant](0,1) to depend on time. Two types of MBM processes were...

Given a geometric Brownian motion S=(St)t[set membership, variant][0,T] and a Borel measurable function such that g(ST)[set membership, variant]L2, we approximate bywhere 0=[tau]0[less-than-or-equals, slant]...[less-than-or-equals, slant][tau]n=T is an increasing sequence of stopping times and...