In this paper, a single-product, single-machine system under Markovian deterioration of machine condition and demand uncertainty is studied.  The objective is to find the optimal intervals for inspection and preventive maintenance activities in a condition-based maintenance planning with discrete monitoring framework. At first, a stochastic dynamic programming model whose state variable is the ...

In this paper at rst, a history of mathematical models is given.Next, some basic information about random variables, stochastic processesand Markov chains is introduced. As follows, the entropy for a discrete timeMarkov process is mentioned. After that, the entropy for SIS stochastic modelsis computed, and it is proved that an epidemic will be disappeared after a longtime.

A dynamic (multi-stage) stochastic programming model for the weekly cost-optimal generation of electric power in a hydro-thermal generation system under uncertain demand (or load) is developed. The model involves a large number of mixed-integer (stochastic) decision variables and constraints linking time periods and operating power units. A stochastic Lagrangian relaxation scheme is designed by...

We derive asymptotic properties for a stochastic dynamic network model in a stochastic dynamic population. In the model, nodes give birth to new nodes until they die, each node being equipped with a social index given at birth. During the life of a node it creates edges to other nodes, nodes with high social index at higher rate, and edges disappear randomly in time. For this model we derive cr...

We consider a class of sampling-based decomposition methods to solve risk-averse multistage stochastic convex programs. We prove a formula for the computation of the cuts necessary to build the outer linearizations of the recourse functions. This formula can be used to obtain an efficient implementation of Stochastic Dual Dynamic Programming applied to convex nonlinear problems. We prove the al...

We begin by reviewing a technique to approximate the dynamics of stochastic programs—written in a stochastic process algebra—by a hybrid system, suitable to capture a mixed discrete/continuous evolution. In a nutshell, the discrete dynamics is kept stochastic while the continuous evolution is given in terms of ODEs, and the overall technique, therefore, naturally associates a Piecewise Determin...

We begin by reviewing a technique to approximate the dynamics of stochastic programs—written in a stochastic process algebra—by a hybrid system, suitable to capture a mixed discrete/continuous evolution. In a nutshell, the discrete dynamics is kept stochastic while the continuous evolution is given in terms of ODEs, and the overall technique, therefore, naturally associates a Piecewise Determin...

We develop a new variant of the recently introduced stochastic transfermatrix DMRG which we call stochastic light-cone corner-transfer-matrix DMRG (LCTMRG). It is a numerical method to compute dynamic properties of onedimensional stochastic processes. As suggested by its name, the LCTMRG is a modification of the corner-transfer-matrix DMRG (CTMRG), adjusted by an additional causality argument. ...

When software reliability demonstration of safety-critical systems by statistical testing is treated as a TAAF (Test, Analyse and Fix) process, an optimal testing policy can be found, which maximises the probability of success of the whole process, over a predetermined period of time. The optimisation problem is formulated, solved by stochastic dynamic programming, and demonstrated by two numer...