An information-theoretic foundation for compound Poisson approximation limit theorems is presented, in analogy to the corresponding developments for the central limit theorem and for simple Poisson approximation. It is shown that the compound Poisson distributions satisfy a natural maximum entropy property within a natural class of distributions. Simple compound Poisson approximation bounds are...

A maximal inequality is an which involves the (absolute) supremum sups⩽t|Xs| or running maximum sups⩽tXs of a stochastic process (Xt)t⩾0. We discuss inequalities for several classes processes with values in Euclidean space: Martingales, Lévy processes, Lévy-type – including Feller (compound) pseudo Poisson stable-like and solutions to SDEs driven by –, strong Markov Gaussian processes. Using Bu...

Manpower Planning is the prerequisite for efficient management of any organization. The stability of the graded structure in corporate and government offices plays a dominant role for efficient planning and control of human resources. The constituent components of a manpower planning model are recruitment process, promotion process and leaving process. This paper addresses a two-graded manpower...

Recent studies have shown that the nonlinear jump-diffusion models give results which are in agreement with financial data. Here we provide linearization criteria together transformations linearize compound Poisson processes. Furthermore, introduce stochastic integrating factor to solve linear equations. Extended Cox–Ingersoll–Ross, Brennan–Schwartz and Epstein be linearizable their explicit so...

This paper focuses on different methods of estimation and forecasting in first-order integer-valued autoregressive processes with Poisson-Lindley (PLINAR(1)) marginal distribution. For this purpose, the parameters of the model are estimated using Whittle, maximum empirical likelihood and sieve bootstrap methods. Moreover, Bayesian and sieve bootstrap forecasting methods are proposed and predict...

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 (0 < p ≤ 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 proces...

While the volatility of portfolios are often modeled by continuous Brownian motion processes, discontinuous jump processes are more appropriate for modeling important external events that significantly affect the prices of financial assets. Here the discontinuous jump processes are modeled by state and control dependent compound Poisson processes, such that the random jumps come at the times of...