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We shall skip a routine derivation of the following result, which provides a stochastic representation of an FL random variable in terms of the above two truncated variables.
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For diffusion processes, the Feynman-Kac formula provides a stochastic representation for solutions to certain second-order partial differential equations (PDEs).
This transformation then provides a stochastic representation (SR) for the random vector uniformly distributed on the tetragon.
In this regard Brownian motion of a single microscopic particle is discussed to intuitively introduce the subject and point out the need for a stochastic representation of the phenomena based on stochastic differential equations (SDEs).
For example, a stochastic representation of a motion pattern can be derived by computing the mean and standard deviation of the sample trajectories [[30]].
The observed incidence for each quartet surrounding a particular SNP type was compared with a stochastic representation of SNP patterns (see Statistics).
The former accounts for the model uncertainty and provides Bayes-optimal predictions; while the latter provides a sparse representation of the stochastic solutions by evaluating the expansion on a subset of dominating gPC bases.
Figure 1 provides a thematic representation of the interview data.
Figure 2 provides a schematic representation of this computational architecture.
Figure 1 provides a graphical representation of the resulting estimates.
Figure 1 provides a graphical representation of the study timelines.
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