Meaning of sample path | Babel Free

Definitions

Any set of possible values to which the appropriate random variables determined by a stochastic process might map a given point in the sample space, taken over all values of the index space (often regarded as time).

Examples

“1968, Leo Breiman, Probability, 1992, Society for Industrial and Applied Mathematics, Unabridged corrected republication, page 298, These processes cannot have versions with continuous sample paths, otherwise the argument given in Chapter 12 forces them to be Brownian motion.”

“1981 [Wiley], Robert J. Adler, The Geometry of Random Fields, 2010, Society for Industrial and Applied Mathematics, Unabridged republication, page 39, In order to study the 'finite' situation it is necessary to impose a number of conditions on the sample paths of the fields. Indeed, what we shall later generally assume is that sample paths belong, with probability one, to the special class of functions we now define.”

“A sample path or stochastic realization of the stochastic process #92;#123;#92;mathcal#123;I#125;(t)#92;#125;#92;infty#95;#123;t#61;0#125; for t#92;in#92;#123;0,#92;Deltat,2#92;Deltat,...#92;#125; is an assignment of a possible value to #92;mathcal#123;I#125;(t) based on the probability vector p(t).[…]Three sample paths of the stochastic model are compared to the deterministic solution in Fig.3.4. One of the sample paths is absorbed before 200 time steps (the population following this path becomes disease-free) but two sample paths are not absorbed during 2,000 time steps.”

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