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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Transition matrices
A finite Markov chain uses a nonnegative matrix with row sums one to describe transitions.
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Markov chains
A Markov chain's next-state distribution depends on the present state rather than the full history.
Stationary distributions
A stationary distribution remains unchanged after applying the chain's transition rule.
Brownian motion
Brownian motion has continuous paths and independent Gaussian increments with variance equal to elapsed time.
Filtrations
An increasing family of sigma-algebras represents information available over time.
Itô calculus
Stochastic integration against Brownian motion includes a quadratic-variation correction in change-of-variable formulas.
Knowledge connections
- Markov chains · Related · Map context
- Stationary distributions · Related · Map context
- Markov chains · Prerequisite · Map context