This paper deals with the Markov modeling and reliability analysis of urea synthesis system of a fertilizer plant. This system was modeled using Markov birth–death process with the assumption that the failure and repair rates of each subsystem follow exponential distribution. The first-order Chapman–Kolmogorov differential equations are developed with the use of mnemonic rule and these equation...

This paper discusses the pricing of CDOs in a Markov chain framework. We show that in general the values of the legs satisfy systems of partial differential equations. In the special case of constant default intensities, one only needs to solve a system of ordinary differential equations, the so-called Kolmogorov differential equations.

The main aim of this work is to establish an averaging principle for a wide class of interacting particle systems of birth-and-death type in the continuum. This principle is an important step in the analysis of Markov evolutions and is usually applied for the associated semigroups related to backward Kolmogorov equations, c.f. [Kur73]. Our approach is based on the study of forward Kolmogorov eq...

This section is devoted to the discussion of two fundamental (partial) differential equations, that arise in the context of Markov diffusion processes. After giving a brief introduction of continuous-time continuous state Markov processes, we introduce the forward and backward equation, and provide a heuristic derivation of these equations for diffusion processes. We also discuss some examples ...

We present results on co-recursive associated Laguerre and Jacobi polynomials which are of interest for the solution of the Chapman-Kolmogorov equations of some birth and death processes with or without absorption. Explicit forms, generating functions, and absolutely continuous part of the spectral measures are given. We derive fourth-order differential equations satisfied by the polynomials wi...

We derive a Feynman-Kac formula for functionals of a stochastic hybrid system evolving according to a piecewise deterministic Markov process. We first derive a stochastic Liouville equation for the moment generator of the stochastic functional, given a particular realization of the underlying discrete Markov process; the latter generates transitions between different dynamical equations for the...

This paper finds fundamental solutions to the backward Kolmogorov equations, usually interpretable as transition density functions for variables x that follow certain stochastic processes of the form dx = A(x, t)dt + cxγdX and dx = A(x, t)dt +α1 +α2x+α3xdX . This is achieved by first reducing the relevant PDEs that the density functions satisfy to their canonical form. These stochastic processe...

This paper deals with the performance analysis of the screening unit in a paper plant using Genetic Algorithm. The screening unit in the paper plant has four main subsystems. These subsystems are arranged in series and parallel configurations. Considering exponential distribution for the probable failures and repairs, the mathematical formulation of the problem is done by Markov birth-death pro...

This paper is a continuation of work commenced in [l] and considers a diffusion in R" given as the solution of a family of stochastic differential equations. The problem discussed is to suppose the direction of the time parameter is reversed, that is, time evolves in anegative direction and the same diffusion process is observed, with the filtration generated by the reversed process. There is a...

This paper deals with the mathematical modeling and performance optimization for the Digesting system of a Paper Plant using Genetic Algorithm. The Digesting system of a Paper Plant has four main subsystems, arranged in series and parallel. Considering exponential distribution for the probable failures and repairs, the mathematical formulation of the problem is done using probabilistic approach...