In this paper we study a storage process or a liquid queue in which the input process is the local time of a positively recurrent stationary diffusion in stationary state and the potential output takes place with a constant deterministic rate. For this storage process we find its stationary...

This article provides a refinement of the main results for the monotone subsequence selection problem, previously obtained by Bruss and Delbaen (Stoch. Proc. Appl. 96 (2001) 313). Let (Ns)s[greater-or-equal, slanted]0 be a Poisson process with intensity 1 defined on the positive half-line. Let...

We use hydrodynamics techniques to study the large deviations properties of the McKean-Vlasov model with singular interactions introduced by Cépa and Lépingle (Probab. Theory Related Fields 107 (1997) 429). In a general framework, we prove upper bounds and exponential tightness, and study the...

The branching random walk (BRW) smoothing transform T is defined as , where given realizations {Xi}i=1L of a point process, U1,U2,... , are conditionally independent identically distributed random variables, and 0[less-than-or-equals, slant]Prob{L=[infinity]}[less-than-or-equals, slant]1. Given...

If the random future evolution of values is modelled in continuous time, then a risk measure can be viewed as a functional on a space of continuous-time stochastic processes. We extend the notions of coherent and convex monetary risk measures to the space of bounded càdlàg processes that are...

We consider simple exclusion processes on for which the underlying random walk has a finite first moment and whose initial distributions are product measures with different densities to the left and to the right of the origin. We prove a strong law of large numbers for the number of particles...

We extend some results on time-homogeneous processes generated by divergence form operators to time-inhomogeneous ones. These results concern the decomposition of such processes as Dirichlet process, with an explicit expression for the term of zero-quadratic variation. Moreover, we extend some...

We study a supercritical branching random walk on a rooted tree with random environment. We are interested in the case where both the branching and the step transition parameters are random quantities. Criteria of (strong) recurrence and (strong) transience are presented for this model.

We study the asymptotic behavior of the empirical distribution function and the empirical process of squared residuals. We prove the Glivenko-Cantelli theorem for the empirical distribution function. We show that the two-parameter empirical process converges to a Gaussian process.

This paper discusses quantitative bounds on the convergence rates of Markov chains, under conditions implying polynomial convergence rates. This paper extends an earlier work by Roberts and Tweedie (Stochastic Process. Appl. 80(2) (1999) 211), which provides quantitative bounds for the total...