Pardoux and Peng (Systems Control Lett. 14 (1990) 55) introduced a class of nonlinear backward stochastic differential equations (BSDEs). According to Pardoux and Peng's theorem, the solution of this type of BSDE consists of a pair of adapted processes, say (y,z). Since then, many researchers...

The spectral structure of discrete time periodically correlated (as well as multivariate stationary) symmetric [alpha]-stable processes is identified by decomposing such a process uniquely in distribution into one sum of three mutually independent periodically correlated (multivariate...

We study the existence of first derivatives with respect to the initial condition of the solution of a finite system of SDEs with reflection. We prove that such derivatives evolve according to a linear differential equation when the process is away from the boundary and that they are projected...

We consider the reflection of an additive process with negative drift controlled by a Markov chain on a finite state space. We determine the tail behaviour of the distribution of the maximum over a regenerative cycle in the case with subexponential increments. Based on this, the asymptotic...

We obtain new conditions for partial sums of an array with stationary rows to converge to a mixture of infinitely divisible distributions with finite variance. More precisely, we show that these conditions are necessary and sufficient to obtain conditional convergence. If the underlying...

We consider how to choose the reproduction rates in a one-dimensional contact process on a finite set to maximize the growth rate of the extinction time with the population size. The constraints are an upper bound on the average reproduction rate, and that the rate profile must be piecewise...

In this paper, we show that the moving average and series representations of fractional Brownian motion can be obtained using the spectral theory of vibrating strings. The representations are shown to be consequences of general theorems valid for a large class of second-order processes with...

We study a unichain Markov decision process i.e. a controlled Markov process whose state process under a stationary policy is an ergodic Markov chain. Here the state and action spaces are assumed to be either finite or countable. When the state process is uniformly ergodic and the immediate cost...

In this paper, we study the problem of the nonparametric estimation of the marginal density f of a class of continuous time processes. To this aim, we use a projection estimator and deal with the integrated mean square risk. Under Castellana and Leadbetter's condition (Stoch. Proc. Appl. 21...

If a Brownian motion is physically constrained to the interval [0,[gamma]] by reflecting it at the endpoints, one obtains an ergodic process whose exponential rate of convergence to equilibrium is [pi]2/2[gamma]2. On the other hand, if Brownian motion is conditioned to remain in (0,[gamma]) up...