Stochastic processes
A stochastic or random process is a collection of random variables that is indexed by some mathematical set (the index set).
Thus, each random variable of the stochastic process is uniquely associated with an element in the set.
A sample function (aka realization) is one outcome that the process generated.
- Bernoulli process
- Wiener process (Brownian motion)
- random walks
- maringales
- Markov processes: next value depends on current value but is independent of previous values (for example: Brownian motion)
- Lévy processes
- Gaussian processes
- random fields
- renewal processes
- branching processes
Techniques used:
- probability
- calculus
- linear algebra
- set theory
- topology