A Gaussian process with Mat�rn covariance has sample paths that are \ lceil \ nu-1 \ rceil times differentiable.
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For another thing, I find it hard to imagine how this totally independent of the length of your sample path.
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At the beam splitter the source light is split into a reference path ( reflected ) and a sampling path ( transmitted onto the sample ).
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Considering that the error reduction in the simulated signal ( using Monte Carlo methods ) has a square root sample paths is required to obtain an accurate result.
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Each trajectory in the figure represents the preference state for one of the risky prospects at each moment in time . Figure 1 Sample paths for a diffusion process
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Modern systems are using pumps instead of flow controllers to provide constant flow rates in a wide flow range with minimum of tubing and a metal free sample path.
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A sample path of a diffusion process models the trajectory of a particle embedded in a flowing fluid and subjected to random displacements due to collisions with molecules, which is called Brownian motion.
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Since reference and sample paths are divergent, this form of interferometer is extremely sensitive to vibration and to atmospheric turbulence in the light paths, both of which interfere with the optical measurements.
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Continuity is a nice property for ( the sample paths of ) a process to have, since it implies that they are well-behaved in some sense, and, therefore, much easier to analyze.
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A more restricted class of processes are the continuous stochastic processes : here the term often ( but not always ) implies both that the index variable is continuous and that sample paths of the process are continuous.
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