Stochastic Processes

Inhaltsverzeichnis

• 1 What is a Stochastic Process?.
• 2 Results from Probability Theory.
• 2.1 Introduction to probability theory.
• 2.2 Bivariate distributions.
• 2.3 Multivariate distributions.
• 2.4 Probability generating functions.
• 2.5 Characteristic functions.
• 3 The Random Walk.
• 3.1 The unrestricted random walk.
• 3.2 Types of stochastic process.
• 3.3 The gambler’s ruin.
• 3.4 Generalisations of the random-walk model.
• 4 Markov Chains.
• 4.1 Definitions.
• 4.2 Equilibrium distributions.
• 4.3 Applications.
• 4.4 Classification of the states of a Markov chain.
• 5 The Poisson Process.
• 6 Markov Chalns with Continuous Time Parameters.
• 6.1 The theory.
• 6.2 Applications.
• 7 Non-Markov Processes in Continuous Time with Discrete State Spaces.
• 7.1 Renewal theory.
• 7.2 Population processes.
• 7.3 Queuing theory.
• 8 Diffusion Processes.
• Recommendations For Further Reading.