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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Queueing processes
Arrival and service mechanisms determine random queue lengths and waiting times.
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Poisson processes
A homogeneous Poisson process counts events with stationary independent increments at a constant rate.
Renewal processes
Independent identically distributed waiting times generate repeated renewal events.
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
- Renewal processes · Related · Map context
- Poisson processes · Related · Map context