sample path

sample path

[′sam·pəl ‚path]
(mathematics)
If {Xt : t in T } is a stochastic process, a sample path for the process is the function on T to the range of the process which assigns to each t the value Xt (w), where w is a previously given fixed point in the domain of the process.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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The Michelson interferometer splits the beam into two different paths: a reference and a sample path. The sample path illuminates a sample and collects the backscattered light.
If t [member of] T is fixed, then [X.sub.t] is a random variable, whereas if we fix e [member of] S, [X.sub.e] is a function of time, called a realization or sample path of the process X(t, e).
Coverage encompasses input analysis, modeling, and estimation; random variate and sample path generation; and output analysis and variance reduction.
* Total sample path length--Many instruments have the option of performing a 20 m and 40 m abrasion path.
The device uses an interferometer with a low coherence diode laser, sending light along two optical paths: the sample path into the eye, and the reference path of the interferometer.
Therefore, while we study the SV-RV model, it is more reasonable to divide the RV into the continuous sample path variation (C) and the discontinuous jump variation (J) and add the two factors into the volatility equation of SV model.
Construct the estimated sample path [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] using the stochastic trend model, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], where the starting value [[??].sup.*.sub.s-1] is set to the observed value [y.sub.s-1].
Sample integrity is protected and carryover effects are mitigated because the entire sample path of the autosampler is chemically inert, and all heated zones of the headspace unit can be set between 30 and 300 C.
A well-known property for Brownian motion on R is that almost every sample path is nowhere differentiable.
For advanced graduate students, Chen provides a systematic account of recent mathematical advances in large deviations arising from the area of sample path intersections, including calculation of the tail probabilities of the intersection local times, the ranges and the intersections of the ranges of random walks and Brownian motions, as well as discussion of the weak law and the law of the iterated logarithm for these models.