Fluctuation properties of compound Poisson-Erlang Lévy processes

Poisson processes , ordinary and compound

The Poisson process is a stochastic counting process that arises naturally in a large variety of daily-life situations. We present a few definitions of the Poisson process and discuss several properties as well as relations to some well-known probability distributions. We further briefly discuss the compound Poisson process.

Alternative Forms of Compound Fractional Poisson Processes

and Applied Analysis 3 where the first term refers to the probability mass concentrated in the origin, δ y denotes the Dirac delta function, and fYβ denotes the density of the absolutely continuous component. The function gYβ given in 1.5 satisfies the following fractional master equation, that is, ∂ ∂tβ gYβ ( y, t ) −λgYβ ( y, t ) λ ∫ ∞ −∞ gYβ ( y − x, t ) fX x dx, 1.6 where ∂/∂t is the Caputo...

Numerical solution and simulation of random differential equations with Wiener and compound Poisson Processes

Ordinary differential equations(ODEs) with stochastic processes in their vector field, have lots of applications in science and engineering. The main purpose of this article is to investigate the numerical methods for ODEs with Wiener and Compound Poisson processes in more than one dimension. Ordinary differential equations with Ito diffusion which is a solution of an Ito stochastic differentia...

Forecasting of compound Erlang demand

Distributional properties of exponential functionals of Lévy processes ∗

We study the distribution of the exponential functional I(ξ, η) = ∫∞ 0 exp(ξt−)dηt, where ξ and η are independent Lévy processes. In the general setting, using the theory of Markov processes and Schwartz distributions, we prove that the law of this exponential functional satisfies an integral equation, which generalizes Proposition 2.1 in [9]. In the special case when η is a Brownian motion wit...