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A Moran process or Moran model is a simple stochastic process used in biology to describe finite populations. The process is named after Patrick Moran, who first proposed the model in 1958. [1] It can be used to model variety-increasing processes such as mutation as well as variety-reducing effects such as genetic drift and natural selection.
A sample function is a single outcome of a stochastic process, so it is formed by taking a single possible value of each random variable of the stochastic process. [ 28 ] [ 139 ] More precisely, if { X ( t , ω ) : t ∈ T } {\displaystyle \{X(t,\omega ):t\in T\}} is a stochastic process, then for any point ω ∈ Ω {\displaystyle \omega \in ...
This list is currently incomplete. 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 ...
Stochastic music was pioneered by Iannis Xenakis, who coined the term stochastic music. Specific examples of mathematics, statistics, and physics applied to music composition are the use of the statistical mechanics of gases in Pithoprakta, statistical distribution of points on a plane in Diamorphoses, minimal constraints in Achorripsis, the ...
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 ...
The first hitting time is defined as the time when the stochastic process first reaches the threshold. It is very important to distinguish whether the sample path of the parent process is latent (i.e., unobservable) or observable, and such distinction is a characteristic of the FHT model. By far, latent processes are most common.
Run-and-tumble motion is a movement pattern exhibited by certain bacteria and other microscopic agents. It consists of an alternating sequence of "runs" and "tumbles": during a run, the agent propels itself in a fixed (or slowly varying) direction, and during a tumble, it remains stationary while it reorients itself in preparation for the next run.
Stochastic chemical kinetics provide yet another example of the use of the master equation. A master equation may be used to model a set of chemical reactions when the number of molecules of one or more species is small (of the order of 100 or 1000 molecules). [ 4 ]