Fractional Poisson processes and related planar random motions

Fractional Poisson Processes and Related Planar Random Motions

We present three different fractional versions of the Poisson process and some related results concerning the distribution of order statistics and the compound Poisson process. The main version is constructed by considering the difference-differential equation governing the distribution of the standard Poisson process, N(t), t > 0, and by replacing the time-derivative with the fractional Dzerba...

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...

Random Planar Structures and Random Graph Processes

Parameter Estimation for Fractional Poisson Processes

The paper proposes a formal estimation procedure for parameters of the fractional Poisson process (fPp). Such procedures are needed to make the fPp model usable in applied situations. The basic idea of fPp, motivated by experimental data with long memory is to make the standard Poisson model more flexible by permitting nonexponential, heavy-tailed distributions of interarrival times and differe...

Fractional Processes: from Poisson to Branching One

Fractional generalizations of the Poisson process and branching Furry process are considered. The link between characteristics of the processes, fractional differential equations and Lèvy stable densities are discussed and used for construction of the Monte Carlo algorithm for simulation of random waiting times in fractional processes. Numerical calculations are performed and limit distribution...