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Markov Processes

This page includes problems and solutions from my Directed Study on "Markov Processes" during the Spring 2016 semester.   
The problems have been taken from the classic book "Elements of the Theory of Markov Processes with Applications" by A. T. Bharucha-Reid. 
Following is the Problem Set:
Problem Set
File Size: 132 kb
File Type: pdf
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Following are the solutions to the individual problems. The topics or concepts the problem touches are written with a "#":

Problem 1
File Size: 126 kb
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# Markov Chain
# Conditional Independence

Problem 2
File Size: 117 kb
File Type: pdf
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# Communicating States

Problem 3
File Size: 97 kb
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# Transient State
# Absorption State
# Recurrent State

Problem 4
File Size: 119 kb
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# Branching Process
​# Generating Functions
# Moments
​# Cumulants

Problem 5
File Size: 105 kb
File Type: pdf
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# Time-Homogeneous Stochastic Process
# Independent Increments
# Differential Equations

Problem 6
File Size: 90 kb
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# Generating Functions
​# Reciprocals

Problem 7
File Size: 124 kb
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# Birth Process
# Partial Differential Equations

Problem 8
File Size: 110 kb
File Type: pdf
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# Periodic Chains
# Limit Matrix

Problem 9
File Size: 127 kb
File Type: pdf
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# Random Walk 
# Functional Independence 
# Recurrence Relation

Problem 10
File Size: 99 kb
File Type: pdf
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# Branching Processes (Fundamental Theorem)
​# Generating Functions
​# Absorption Probabilities

Problem 11
File Size: 100 kb
File Type: pdf
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# Birth-and-Death Process
# Conditional Expected Time

Problem 12
File Size: 127 kb
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# Coefficient of Variation
# Poisson Process
# Simple Birth Process
​# Birth-and-Death Process

Full Solution Set
File Size: 204 kb
File Type: pdf
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