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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A homogeneous Poisson process counts events with stationary independent increments at a constant rate.
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Brownian motion has continuous paths and independent Gaussian increments with variance equal to elapsed time.
An increasing family of sigma-algebras represents information available over time.
Arrival and service mechanisms determine random queue lengths and waiting times.
A stochastic process is a time-indexed collection of random variables.
Stochastic integration against Brownian motion includes a quadratic-variation correction in change-of-variable formulas.
Explore processes and dependence; counting and continuous paths; information and stochastic calculus. Concepts and connections are available independently of video coverage.