Sentence examples for defined by the stochastic from inspiring English sources

Analogously, a diffusion process for the state variable X t can be defined by the stochastic equation d X t = 2 D d W t, (12).

If we assume that (A0) holds, then the functions defined by the stochastic representations (12) and (14) are smooth and classical solutions to the systems of parabolic equations (13) and (15), respectively; see [2] for further details.

The second class of bivariate beta distribution is defined by the stochastic representation, Z 1, Z 2 ⊤ = G a 1 G a 1 + G a 3, G a 2 G a 2 + G a 3 + G a 4 ⊤.

The first class of bivariate beta distribution is defined by the stochastic representation, Z 1, Z 2 ⊤ = G a 1 G a 1 + G b, G a 2 G a 2 + G b ⊤. (3).

The first class of bivariate BG distribution is defined by the stochastic representation, X 1, X 2 ⊤ = F 1 - 1 G a 1 G a 1 + G b, F 2 - 1 G a 2 G a 2 + G b ⊤, (4).

The second class of bivariate BG distribution is defined by the stochastic representation, X 1, X 2 ⊤ = F 1 - 1 G a 1 G a 1 + G a 3, F 2 - 1 G a 2 G a 2 + G a 3 + G a 4 ⊤, (9).

Diffusion processes X defined by the following stochastic differential equation are considered in this article: begin{aligned}& dX_{t}=mu (X_{t}),dt+sigma (X_{t}),dB_{t}, end{aligned} (1) where ({B_{t}, tge 0}) is a standard Brownian motion, (mu (cdot)) is an unknown measurable function (drift function) and (sigma ( cdot)) is an unknown positive function (diffusion function).

The clusters identified by the MCL are defined by simulating the stochastic flow within the networks [ 16].

The random field is then treated as a random displacement applied to the conductors defined by the mean geometry, to derive the stochastic Lagrangian boundary integral equation.

Note that under this frequentist approach to network reconstruction, we interpret the data to be a (possibly censored) realization from the stochastic network defined by the joint probability law given above.

The model simulates the mobility of individuals between these subpopulations using a stochastic procedure defined by the airline transportation data [ 6].