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Examples of such stochastic processes include the Wiener process or Brownian motion process, [a] used by Louis Bachelier to study price changes on the Paris Bourse, [21] and the Poisson process, used by A. K. Erlang to study the number of phone calls occurring in a certain period of time. [22]
Examples include a stochastic matrix, which describes a stochastic process known as a Markov process, and stochastic calculus, which involves differential equations and integrals based on stochastic processes such as the Wiener process, also called the Brownian motion process.
See also Category:Stochastic processes. Basic affine jump diffusion; Bernoulli process: discrete-time processes with two possible states. Bernoulli schemes: discrete-time processes with N possible states; every stationary process in N outcomes is a Bernoulli scheme, and vice versa. Bessel process; Birth–death process; Branching process ...
[35] [36] Two important examples of Markov processes are the Wiener process, also known as the Brownian motion process, and the Poisson process, [19] which are considered the most important and central stochastic processes in the theory of stochastic processes.
Sample-continuous process; Sazonov's theorem; Schramm–Loewner evolution; Self-similar process; Single-particle trajectory; Spherical contact distribution function; Spitzer's formula; Stationary increments; Stationary process; Statistical fluctuations; Stochastic control; Stochastic differential equation; Stochastic geometry; Stochastic ...
In probability theory, a martingale is a sequence of random variables (i.e., a stochastic process) for which, at a particular time, the conditional expectation of the next value in the sequence is equal to the present value, regardless of all prior values. Stopped Brownian motion is an example of a martingale. It can model an even coin-toss ...
If a stochastic process is strict-sense stationary and has finite second moments, it is wide-sense stationary. [2]: p. 299 If two stochastic processes are jointly (M + N)-th-order stationary, this does not guarantee that the individual processes are M-th- respectively N-th-order stationary. [1]: p. 159
In mathematics, a stopped process is a stochastic process that is forced to assume the same value after a prescribed (possibly random) time. Definition [ edit ]