The aim of this paper is to establish Strassen's law of the iterated logarithm for negatively associated random vectors under the finite second moment.

For processes X(t),t0 governed by signed measures whose density is the fundamental solution of third and fourth-order heat-type equations (higher-order diffusions) the explicit form of the joint distribution of (max0[less-than-or-equals, slant]s[less-than-or-equals, slant]t X(s),X(t)) is...

This paper obtains a uniform reduction principle for the empirical process of a stationary moving average time series {Xt} with long memory and independent and identically distributed innovations belonging to the domain of attraction of symmetric [alpha]-stable laws, 1[alpha]2. As a consequence,...

The aim of this paper is to study the behavior of solutions of some nonlinear partial differential equations of Mac Kean-Vlasov type. The main tools used are, on one hand, the logarithmic Sobolev inequality and its connections with the concentration of measure and the transportation inequality...

In this paper, we consider a risk model with stochastic return on investments. We mainly discuss the ruin probability, the surplus distribution at the time of ruin and the supremum distribution of the surplus before ruin. We prove some properties for these distributions and derive the...

We discuss Brownian analogues of a celebrated theorem, due to Burke, which states that the output of a (stable, stationary) M/M/1 queue is Poisson, and the related notion of quasireversibility. A direct analogue of Burke's theorem for the Brownian queue was stated and proved by Harrison...

In this paper, we study the moderate deviation principle of an inhomogeneous integral functional of a Markov process ([xi]s) which is exponentially ergodic, i.e. the moderate deviations ofin the space of continuous functions from [0,1] to , where f is some -valued bounded function. Our method...

Let {bF(t),t[set membership, variant][0,1]} be an F-Brownian bridge process. We study the asymptotic behaviour of non-linear functionals of regularizations by convolution of this process and apply these results to the estimation of the variance of a non-homogeneous diffusion and to the...

We consider one-dimensional differential equations with a boundary condition on the interval [0,1], perturbed by a Poisson noise. We study existence and uniqueness, the law of the solution and in which cases the solution is a reciprocal process.

Let {X(t); 0[less-than-or-equals, slant]t[less-than-or-equals, slant]1} be a real-valued continuous Gaussian Markov process with mean zero and covariance [sigma](s,t)=EX(s)X(t)[not equal to]0 for 0<s, t<1. It is known that we can write [sigma](s,t)=G(min(s,t))H(max(s,t)) with G>0, H0 and G/H nondecreasing on the interval (0,1). We show that for the Lp-norm on C[0,1],...</s,>