Table of Contents
1 Cover
4 Preface
7 PART 1: Basic Methods 1 Preliminary Concepts 1.1. Introduction to random evolutions 1.2. Abstract potential operators 1.3. Markov processes: operator semigroups 1.4. Semi-Markov processes 1.5. Lumped Markov chains 1.6. Switched processes in Markov and semi-Markov media 2 Homogeneous Random Evolutions (HRE) and their Applications 2.1. Homogeneous random evolutions (HRE) 2.2. Limit theorems for HRE
8 PART 2: Applications to Reliability, Random Motions, and Telegraph Processes 3 Asymptotic Analysis for Distributions of Markov, Semi-Markov and Random Evolutions 3.1. Asymptotic distribution of time to reach a level that is infinitely increasing by a family of semi-Markov processes on the set ℕ; 3.2. Asymptotic inequalities for the distribution of the occupation time of a semi-Markov process in an increasing set of states 3.3. Asymptotic analysis of the occupation time distribution of an embedded semi-Markov process (with increasing states) in a diffusion process 3.4. Asymptotic analysis of a semigroup of operators of the singularly perturbed random evolution in semi-Markov media 3.5. Asymptotic expansion for distribution of random motion in Markov media under the Kac condition 3.6. Asymptotic estimation for application of the telegraph process as an alternative to the diffusion process in the Black–Scholes formula 4 Random Switched Processes with Delay in Reflecting Boundaries 4.1. Stationary distribution of evolutionary switched processes in a Markov environment with delay in reflecting boundaries 4.2. Stationary distribution of switched process in semi-Markov media with delay in reflecting barriers 4.3. Stationary efficiency of a system with two unreliable subsystems in cascade and one buffer: the Markov case 4.4. Application of random evolutions with delaying barriers to modeling control of supply systems with feedback: the semi-Markov switching process 5 One-dimensional Random Motions in Markov and Semi-Markov Media 5.1. One-dimensional semi-Markov evolutions with general Erlang sojourn times 5.2. Distribution of limiting position of fading evolution 5.3. Differential and integral equations for jump random motions 5.4. Estimation of the number of level crossings by the telegraph process
10 Index
List of Illustrations
1 Chapter 4Figure 4.1. A system of two unreliable subsystems, say S1 and S2, connected in s...Figure 4.2. Efficiency parameter K as a function of reservoir size V for differe...Figure 4.3. Efficiency parameter K as a function of reservoir size V for differe...
List of Tables
1 Chapter 4Table 4.1. Maximum and minimum values of K for different λ/μ ratios. We have fix...Table 4.2. Maximum values of K at V = 5 for different λ/μ ratios and different v...
Guide
1 Cover
5 Preface
