Compound Poisson Disorder Problem

Compound Poisson Disorder Problems with Nonlinear Detection Delay Penalty Cost Functions

The quickest detection of the unknown and unobservable disorder time, when the arrival rate and mark distribution of a compound Poisson process suddenly changes, is formulated in a Bayesian setting, where the detection delay penalty is a general smooth function of the detection delay time. Under suitable conditions, the problem is shown to be equivalent to the optimal stopping of a finite-dimen...

The Disorder Problem for Compound Poisson Processes with Exponential Jumps

The problem of disorder seeks to determine a stopping time which is as close as possible to the unknown time of ’disorder’ when the observed process changes its probability characteristics. We give a partial answer to this question for some special cases of Lévy processes and present a complete solution of the Bayesian and variational problem for a compound Poisson process with exponential jump...

THE DISORDER PROBLEM FOR COMPOUND POISSON PROCESSES WITH EXPONENTIAL JUMPS BY PAVEL V. GAPEEV Russian Academy of Sciences

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...

A two-sided exit problem for a difference of a compound Poisson process and a compound renewal process with a discrete phase space

Abstract A two-sided exit problem is solved for a difference of a compound Poisson process and a compound renewal process. The Laplace transforms of the joint distribution of the first exit time, the value of the overshoot and the value of a linear component at this instant are determined. The results obtained are applied to solve the two-sided exit problem for a particular case of this process...