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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An increasing family of sigma-algebras represents information available over time.
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Itô calculus
Stochastic integration against Brownian motion includes a quadratic-variation correction in change-of-variable formulas.
Martingales
An integrable adapted process has conditional expected future value equal to its present value.
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.
Brownian motion
Brownian motion has continuous paths and independent Gaussian increments with variance equal to elapsed time.
Knowledge connections
- Martingales · Related · Map context
- Itô calculus · Related · Map context
- Poisson processes · Related · Map context
- Random variables · Related · Map context
- Martingales · Next concept · Map context