WJWJ Maths
Stochastic Processes
  • Warming Up
  • Examples on Probability
  • Conditional Expectation
  • Computing Expectations by Conditioning
  • Computing Probability by Conditioning
  • Markov’s Inequality
  • Computing Variance by Conditioning
  • Stochastic Process
  • Definitions
  • Markovian Stochastic Process
  • Homogeneous Markov Processes
  • Markov Chains
  • Introduction
  • Chapman Kolmogrov Equations
  • Unconditional Distributions
  • Classification of States
  • Random Walk Models
  • One Dimensional Random Walk
  • Two Dimensional Symmetrical Random Walk
  • Three Dimensional Symmetric Random Walk
  • Limiting probabilities
  • Expected Number of Visits
  • Expected Number of Visists to a Transient State
  • Branching Process
  • Stochastic Process with Continuous Time
  • Poisson Process
  • Interarrival and Waiting Time Distributions
  • Further Properties of Poisson Process
  • Birth and Death Process
  • The Simple Birth Process
  • Simple Death Process
  • Simple Birth and Death Process
  • Effects of Immigration
  • Queues (Consider a Markov Chain with continuous time)
  • Brownian Motion
  • REFERENCES
  • Practice Problems

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Chapter 1
Warming Up

1.1 Examples on Probability
1.2 Conditional Expectation
1.3 Computing Expectations by Conditioning
1.4 Computing Probability by Conditioning
1.5 Markov’s Inequality
1.6 Computing Variance by Conditioning

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