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Applications and the study of phenomena have in turn inspired the proposal of new stochastic processes. 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 ...
Stochastic social science theory is similar to systems theory in that events are interactions of systems, although with a marked emphasis on unconscious processes. The event creates its own conditions of possibility, rendering it unpredictable if simply for the number of variables involved.
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.
An example of a discrete-time stationary process where the sample space is also discrete (so that the random variable may take one of N possible values) is a Bernoulli scheme. Other examples of a discrete-time stationary process with continuous sample space include some autoregressive and moving average processes which are both subsets of the ...
For example, the emission of radiation from atoms is a natural stochastic process. It can be simulated directly, or its average behavior can be described by stochastic equations that can themselves be solved using Monte Carlo methods.
An example of a stochastic process which is not a Markov chain is the model of a machine which has states A and E and moves to A from either state with 50% chance if it has ever visited A before, and 20% chance if it has never visited A before (leaving a 50% or 80% chance that the machine moves to E).
Suppose that , [,] is given, and we wish to compute .Stochastic computing performs this operation using probability instead of arithmetic. Specifically, suppose that there are two random, independent bit streams called stochastic numbers (i.e. Bernoulli processes), where the probability of a 1 in the first stream is , and the probability in the second stream is .