Stochastic Processes
Explore processes and dependence; counting and continuous paths; information and stochastic calculus. Concepts and connections are available independently of video coverage.
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Martingales
An integrable adapted process has conditional expected future value equal to its present value.
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Filtrations
An increasing family of sigma-algebras represents information available over time.
Stopping times
Whether a stopping time has occurred by a time is determined by information available then.
Brownian motion
Brownian motion has continuous paths and independent Gaussian increments with variance equal to elapsed time.
Itô calculus
Stochastic integration against Brownian motion includes a quadratic-variation correction in change-of-variable formulas.
Markov chains
A Markov chain's next-state distribution depends on the present state rather than the full history.
Knowledge connections
- Filtrations · Related · Map context
- Stopping times · Related · Map context
- Filtrations · Prerequisite · Map context