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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Stochastic processes
A stochastic process is a time-indexed collection of random variables.
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Markov chains
A Markov chain's next-state distribution depends on the present state rather than the full history.
Poisson processes
A homogeneous Poisson process counts events with stationary independent increments at a constant rate.
Random variables
A random variable is a measurable function on a probability space, allowing outcomes to be described numerically.
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.
Knowledge connections
- Markov chains · Related · Map context
- Stationary distributions · Related · Map context
- Random variables · Related · Map context
- Poisson processes · Related · Map context
- Random variables · Prerequisite · Map context