By Vrbik J.
This path used to be learn in Brock collage through Jan Vrbik.
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Extra info for Introduction to stochastic processes (lecture notes)
Sample text
Brownian motion, indeed, represents the simplest possible stochastic differential equation. This raises one of the main ideas to be explored in this book: that just as "real" Brownian motion is intimately connected with molecular scale diffusion, pore-scale Brownian motion may be used as a model of dispersion in a porous medium. In this way we will show that Fickian assumptions may be avoided and a more fundamental description addressing, for example, the scale dependence problem can be attempted.
Serrano (1996) solved the three-dimensional solute continuity equation in a large domain neglecting the micro diffusion and using a decomposition method. However, the probability law of the velocity fields needs to be provided to solve the solute transport equation for a particular aquifer. 7 Computational Modeling of Transport in Porous Media As we have seen in the previous discussion on the solute transport in heterogeneous media, the problem of predicting the solute concentration of a plume is complicated by many factors.
T+t 0 Similarly a left-continuous function at to can be represented as f (t-)= limf (t)=f (to). t~t 0 These statements imply that a continuous function in both right-continuous and left-continuous at a given point of t. Often we encounter functions having discontinuities; hence the need for the above definitions. To measure the size of a discontinuity, we define the term "jump" at any point t to be a discontinuity where the both fit+) and fit-) exist and the size of the jump be A f ( t ) = f ( t + ) - f ( t - ) .
Introduction to stochastic processes (lecture notes) by Vrbik J.
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