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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Itô calculus
Stochastic integration against Brownian motion includes a quadratic-variation correction in change-of-variable formulas.
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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.
Markov chains
A Markov chain's next-state distribution depends on the present state rather than the full history.
Martingales
An integrable adapted process has conditional expected future value equal to its present value.
Knowledge connections
- Stopping times · Related · Map context
- Filtrations · Related · Map context