Applied Stochastic Processes 1st Edition by Ming Liao ISBN 1466589345 9781466589346

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ISBN 10: 1466589345 
ISBN 13: 9781466589346
Author: Ming Liao

Applied Stochastic Processes 1st Table of contents:

Chapter 1 Probability and stochastic processes
1.1 Probability
1.2 Random variables and their distributions
1.3 Mathematical expectation
1.4 Joint distribution and independence
Proposition 1.1
1.5 Convergence of random variables
1.6 Laplace transform and generating functions
1.7 Examples of discrete distributions
1.8 Examples of continuous distributions
1.9 Stochastic processes
1.10 Stopping times
Theorem 1.2.
Example 1.3.
Exercise 1.1
Exercise 1.2
Exercise 1.3
1.11 Conditional expectation
Proof of (1.22):
Example 1.4.
Example 1.5.
Example 1.6.
Example 1.7.
Exercise 1.4
Exercise 1.5
Exercise 1.6
Exercise 1.7
Exercise 1.8
Exercise 1.9
Chapter 2 Poisson processes
2.1 Introduction to Poisson processes
Theorem 2.1
Theorem 2.2
Example 2.3.
Exercise 2.1
Exercise 2.2
2.2 Arrival and inter-arrival times of Poisson processes
Example 2.4.
Theorem 2.5
Theorem 2.6
Example 2.7.
Exercise 2.3
Exercise 2.4
Exercise 2.5
2.3 Conditional distribution of arrival times
Theorem 2.8
Example 2.9.
Example 2.10.
Theorem 2.11
Example 2.12.
Exercise 2.6
Exercise 2.7
Exercise 2.8
Exercise 2.9
Exercise 2.10
2.4 Poisson processes with different types of events
Theorem 2.13
Example 2.14.
Exercise 2.11
Exercise 2.12
2.5 Compound Poisson processes
Theorem 2.15
Example 2.16.
Exercise 2.13
Exercise 2.14
2.6 Nonhomogeneous Poisson processes
Theorem 2.17
Theorem 2.18
Example 2.19.
Exercise 2.15
Exercise 2.16
Exercise 2.17
Chapter 3 Renewal processes
3.1 An introduction to renewal processes
Example 3.1.
Theorem 3.2.
Theorem 3.3.
Theorem 3.4.
Exercise 3.1.
Exercise 3.2.
Exercise 3.3.
Exercise 3.4.
3.2 Renewal reward processes
Theorem 3.5.
Theorem 3.6.
Example 3.7.
Example 3.8.
Example 3.9.
Example 3.10.
Exercise 3.5.
Exercise 3.6.
Exercise 3.7.
Exercise 3.8.
Exercise 3.9.
Exercise 3.10.
3.3 Queuing systems
Theorem 3.11.
Lemma 3.12.
FIGURE 3.1: Total queue length of a queuing system.
3.4 Queue lengths, waiting times, and busy periods
Proposition 3.13
Proposition 3.14
Theorem 3.15.
Theorem 3.16.
Theorem 3.17.
Exercise 3.11.
Exercise 3.12.
Exercise 3.13.
Exercise 3.14.
Exercise 3.15.
3.5 Renewal equation
Theorem 3.18.
Proposition 3.19
Theorem 3.20.
Example 3.21.
Exercise 3.16.
Exercise 3.17.
Exercise 3.18.
Exercise 3.19.
3.6 Key renewal theorem
Theorem 3.22.
Example 3.23.
Theorem 3.24.
Theorem 3.25.
Exercise 3.20.
Exercise 3.21.
Exercise 3.22.
Exercise 3.23.
3.7 Regenerative processes
Theorem 3.26.
Theorem 3.27.
3.8 Queue length distribution and PASTA
Theorem 3.28.
Theorem 3.29.
Theorem 3.30.
Lemma 3.31.
Theorem 3.32.
Exercise 3.24.
Exercise 3.25.
Exercise 3.26.
Chapter 4 Discrete time Markov chains
4.1 Markov property and transition probabilities
Exercise 4.1
Exercise 4.2
Exercise 4.3
4.2 Examples of discrete time Markov chains
Example 4.1.
Example 4.2.
Example 4.3.
Example 4.4.
Example 4.5.
Exercise 4.4
Exercise 4.5
Exercise 4.6
4.3 Multi-step transition and reaching probabilities
Example 4.6.
Exercise 4.7
Exercise 4.8
Exercise 4.9
4.4 Classes, recurrence, and transience
Theorem 4.7
Example 4.8.
Example 4.9.
Example 4.10.
Theorem 4.11
FIGURE 4.1: Graphs of P(s).
Exercise 4.10
Exercise 4.11
Exercise 4.12
Exercise 4.13
4.5 Periodicity, class property, and positive recurrence
Theorem 4.12
Lemma 4.13
Theorem 4.14
Example 4.15.
Theorem 4.16
Exercise 4.14
Exercise 4.15
4.6 Expected hitting time and hitting probability
Theorem 4.17
Example 4.18.
Example 4.19.
Example 4.20.
Exercise 4.16
Exercise 4.17
Exercise 4.18
Exercise 4.19
4.7 Stationary distribution
Theorem 4.21
Theorem 4.22
Example 4.23.
Example 4.24.
Example 4.25.
Example 4.26.
Theorem 4.27
Exercise 4.20
Exercise 4.21
Exercise 4.22
Exercise 4.23
Exercise 4.24
4.8 Limiting properties
Theorem 4.28
Corollary 4.29
Lemma 4.30
Theorem 4.31
Theorem 4.32
Corollary 4.33
Theorem 4.34
Theorem 4.35
Example 4.36.
Exercise 4.25
Exercise 4.26
Exercise 4.27
Chapter 5 Continuous time Markov chain
5.1 Markov property and transition probability
5.2 Transition rates
Theorem 5.1
Theorem 5.2
Transition rate
Theorem 5.3
Example 5.4.
Exercise 5.1
Exercise 5.2
Exercise 5.3
5.3 Stationary distribution and limiting properties
Theorem 5.5
Theorem 5.6
Example 5.7.
Uniformization
Example 5.8.
Exercise 5.4
Exercise 5.5
Exercise 5.6
Exercise 5.7
5.4 Birth and death processes
Theorem 5.9
Example 5.10.
Example 5.11.
Exercise 5.8
Exercise 5.9
Exercise 5.10
5.5 Exponential queuing systems
Example 5.12.
Theorem 5.13
Exercise 5.11
Exercise 5.12
Exercise 5.13
Exercise 5.14
Exercise 5.15
5.6 Time reversibility
Theorem 5.14
Proposition 5.15
Theorem 5.16
Example 5.17.
Example 5.18.
Example 5.19.
Two queuing systems in tandem
Theorem 5.20
Example 5.21.
Example 5.22.
Exercise 5.16
Exercise 5.17
Exercise 5.18
Exercise 5.19
Exercise 5.20
5.7 Hitting time and phase-type distributions
Example 5.23.
Exercise 5.21
Exercise 5.22
5.8 Queuing systems with time-varying rates
Example 5.24.
FIGURE 5.1: The expected total queue length in M(t)/M(t)/2/4
Theorem 5.25
Example 5.26.
FIGURE 5.2: Graphs of ρ(t) and ρ*(t).
FIGURE 5.3: Expected total queue length.
Chapter 6 Brownian motion and beyond
6.1 Brownian motion
Theorem 6.1.
Exercise 6.1.
Exercise 6.2.
Exercise 6.3.
6.2 Standard Brownian motion and its maximum
Theorem 6.2.
FIGURE 6.1: A reflected path.
Example 6.3.
Exercise 6.4.
Exercise 6.5.
6.3 Conditional expectation and martingales
6.4 Brownian motion with drift
Proposition 6.4
Theorem 6.5.
Theorem 6.6.
Example 6.7.
Exercise 6.6.
Exercise 6.7.
6.5 Stochastic integrals
6.6 Itô’s formula and stochastic differential equations
Example 6.8.
Exercise 6.8.
Exercise 6.9.
Exercise 6.10.
Exercise 6.11.
6.7 A single stock market model
Theorem 6.9.
Theorem 6.10.
Example 6.11.
Example 6.12.

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Tags: Ming Liao, Stochastic, Processes