Related papers: Observing a L\'evy process up to a stopping time

Computational complexity is examined using the principle of increasing entropy. To consider computation as a physical process from an initial instance to the final acceptance is motivated because many natural processes have been recognized…

A characterization of mixed Poisson processes in terms of disintegrations is proven. As a consequence some further characterizations of such processes via claim interarrival processes, martingales and claim measures are obtained. Some…

We offer a unified approach to the theory of convex minorants of L\'{e}vy processes with continuous distributions. New results include simple explicit constructions of the convex minorant of a L\'{e}vy process on both finite and infinite…

We prove several results concerning classifications, based on successive observations $(X_1,..., X_n)$ of an unknown stationary and ergodic process, for membership in a given class of processes, such as the class of all finite order Markov…

The natural analogue for a Levy process of Cramer's estimate for a reflected random walk is a statement about the exponential rate of decay of the tail of the characteristic measure of the height of an excursion above the minimum. We…

Although introduced in the case of Poisson random measures, the lent particle method applies as well in other situations. We study here the case of marked point processes. In this case the Malliavin calculus (here in the sense of Dirichlet…

We review some recent results of quantitative long-time convergence for the law of a killed Markov process conditioned to survival toward a quasi-stationary distribution, and on the analogous question for the particle systems used in…

This paper presents an identity between the multivariate and univariate saddlepoint approximations applied to sample path probabilities for a certain class of stochastic processes. This class, which we term the recursively compounded…

A compound Poisson process whose randomized time is an independent Poisson process is called compound Poisson process with Poisson subordinator. We provide its probability distribution, which is expressed in terms of the Bell polynomials,…

We prove a new theorem on additive Levy processes and show that this theorem implies several proved theorems and a hard conjectured theorem.

Generalizing earlier works of Delbaen & Haezendonck [5] as well as of [18] and [16] for given compound mixed renewal process S under a probability measure P, we characterize all those probability measures Q on the domain of P such that Q…

Different change-point type models encountered in statistical inference for stochastic processes give rise to different limiting likelihood ratio processes. In a previous paper of one of the authors it was established that one of these…

A method is developed to estimate the parameters of a Levy copula of a discretely observed bivariate compound Poisson process without knowledge of common shocks. The method is tested in a small sample simulation study. Also, the method is…

Various recent results on quantum L\'evy processes are presented. The first part provides an introduction to the theory of L\'evy processes on involutive bialgebras. The notion of independence used for these processes is tensor…

The problem is sequence prediction in the following setting. A sequence $x_1,...,x_n,...$ of discrete-valued observations is generated according to some unknown probabilistic law (measure) $\mu$. After observing each outcome, it is required…

We study a real-valued L\'evy-type process $X$, which is locally $\alpha$-stable in the sense that its jump kernel is a combination of a `principal' (state dependent) $\alpha$-stable part with a `residual' lower order part. We show that…

We study the relativistic Vlasov-Maxwell system which describes large systems of particles interacting by means of their collectively generated forces. If the speed of light $c$ is considered as a parameter then it is known that in the…

In the compulsive gambler process there is a finite set of agents who meet pairwise at random times ($i$ and $j$ meet at times of a rate-$\nu_{ij}$ Poisson process) and, upon meeting, play an instantaneous fair game in which one wins the…

Theoretical analysis proves that human survivability is dominated by an unusual physical, rather than biological, mechanism, which yields an exact law. The law agrees with all experimental data, but, contrary to existing theories, it is the…

We analyze extensions of the Poisson process in which any interarrival time that exceeds a fixed value $r$ is counted as an interarrival of duration $r$. In the engineering application that initiated this work, one part is tested at a time,…