We investigate the connections between the mean pathwise regularity of stochastic processes and their L r (P)-functional quantization rate as random variables taking values in some L p ([0, T ], dt)-spaces (< 0p ≤ r). Our main tool is the Haar basis. We then emphasize that the derived functional quantization rate may be optimal (like for the Brownian motion) or not (like for the Poisson process...

The excursion{set, Press{Schechter mass spectrum for a Poisson distribution of identical particles is derived. For the special case of an initially Poisson distribution the spatial distribution of the Press{Schechter clumps is shown to be Poisson. Thus, the distribution function of particle counts in randomly placed cells is easily obtained from the Press{Schechter multiplicity function. This P...

In this paper we consider the probabilities of finiteand infinite-time absolute ruin in the renewal risk model with constant premium rate and constant force of interest. In the particular case of compound Poisson model, explicit asymptotic expressions for the finiteand infinite-time absolute ruin probabilities are given. For the general renewal risk model, we present an asymptotic expression fo...

We present an overview of existing methods to generate pseudorandom numbers from a nonhomogeneous Poisson process. We start with various definitions of the nonhomogeneous Poisson process, present theoretical results (sometimes with a proof) that form the basis of existing generation algorithms, and provide algorithm listings. Whenever available, we also provide links to sources containing compu...

Dufresne et al. (1991) introduced a general risk model defined as the limit of compound Poisson processes. Such model is either a compound Poisson process itself or a strictly increasing Lévy process. Their construction is based on a nonnegative non-increasing function Q that governs the jumps of the process. This function, it turns out, is the tail of the Lévy measure of the process. We discus...

We consider a continuous review inventory system that faces two different cases of demand processes. In one case demand follows a compound Poisson process. In the other case demand is a combination of a constant deterministic component and a random component which follows a compound Poisson process. We assume negligible lead time. Orders occur when inventory level drops to or below level zero, ...

We present an overview of existing methods to generate pseudorandom numbers from homogeneous Poisson processes. We provide three well-known definitions of the homogeneous Poisson process, present results that form the basis of various existing generation algorithms, and provide algorithm listings. With the intent of guiding users seeking an appropriate algorithm for a given setting, we note the...

What constitutes jointly Poisson processes remains an unresolved issue. This report reviews the current state of the theory and indicates how the accepted but unproven model equals that resulting from the small time-interval limit of jointly Bernoulli processes. One intriguing consequence of these models is that jointly Poisson processes can only be positively correlated as measured by the corr...

For the continuous-time risk model with compound Poisson input, the ((nite-horizont) joint probability P (t; X x; Y y) of ruin time , surplus X just before ruin and deecit Y at ruin time is considered as a function of the arrival rate of claims. It is expanded into a Taylor series at = 0. A certain extension of a corresponding result for innnite-horizont joint probabilities, which previously ha...

C-control chart assumes that process nonconformities follow a Poisson distribution. In actuality, however, this Poisson distribution does not always occur. A process control for semiconductor based on a Poisson distribution always underestimates the true average amount of nonconformities and the process variance. Quality is described more accurately if a compound Poisson process is used for pro...