This paper considers a stable GI/GI/1 queue with subexponential service time distribution. Under natural assumptions we derive the tail behaviour of the busy period of this queue. We extend the results known for the regular variation case under minimal conditions. Our method of proof is based on...

This paper investigates a mixed regular-singular stochastic control problem where the drift of the dynamics is quadratic in the regular control variable. More importantly, the regular control variable is constrained. The value function of the problem is derived in closed form via solving the...

A risk process with delay in claim settlement is usually described in terms of a Poisson shot-noise process (see Klüppelberg and Mikosch (Bernoulli 1 (1995) 125) and Brémaud (Appl. Probab. 37 (2000) 914)). In particular, proves that under suitable conditions the corresponding ruin probability...

We suggest a discrete-time approximation for decoupled forward-backward stochastic differential equations. The Lp norm of the error is shown to be of the order of the time step. Given a simulation-based estimator of the conditional expectation operator, we then suggest a backward simulation...

In this work we introduce correlated random walks on . When picking suitably at random the coefficient of correlation, and taking the average over a large number of walks, we obtain a discrete Gaussian process, whose scaling limit is the fractional Brownian motion. We have to use two radically...

We derive the exact asymptotic behavior of the ruin probability P{X(t)x for some t0} for the process , with respect to level x which tends to infinity. We assume that the underlying process [xi](t) is a.s. continuous stationary Gaussian with mean zero and correlation function regularly varying...

Consider the stochastic Duffing-van der Pol equationwith A[greater-or-equal, slanted]0 and B0. If [beta]/2+[sigma]2/8[omega]20 then for small enough [var epsilon]0 the system is positive recurrent in R2[-45 degree rule]{0}. Let denote the top Lyapunov exponent for the linearization of this...

In this paper, we study a class of multi-dimensional backward stochastic differential equations (BSDEs, for short) in which the terminal values and the generators are allowed to be "discrete-functionals" of a forward diffusion. We first establish some new types of Feynman-Kac formulas related to...

We study the small deviation problem for a class of symmetric Lévy processes, namely, subordinated Lévy processes. These processes can be represented as WoA, where W is a standard Brownian motion, and A is a subordinator independent of W. Under some mild general assumption, we give precise...

Hölder estimates are given for the solutions of parabolic stochastic partial differential equations in C1 domains. Also existence and uniqueness theorems are presented in Lp-spaces with weights. It is allowed that the powers of summability with respect to space and time to be different.