Continuous stochastic process

<p>In <a href="/facts/Probability_theory/mFBn51rE">probability theory</a>, a continuous stochastic process is a type of <a href="/facts/Stochastic_process/Ng1n1dnB">stochastic process</a> that may be said to be "<a href="/facts/Continuous_function/sKbl02pB">continuous</a>" as a function of its "time" or index parameter. Continuity is a nice property for (the sample paths of) a process to have, since it implies that they are <a href="/facts/Well-behaved/KmKHjJ1H">well-behaved</a> in some sense, and, therefore, much easier to analyze. It is implicit here that the index of the stochastic process is a continuous variable. Some authors define a "continuous (stochastic) process" as only requiring that the index variable be continuous, without continuity of sample paths: in another terminology, this would be a <a href="/facts/Continuous-time_stochastic_process/HDwC9wg8">continuous-time stochastic process</a>, in parallel to a "discrete-time process". Given the possible confusion, caution is needed.
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Continuous stochastic process open-in-new

Continuous stochastic process