Search results
In probability theory and statistics, diffusion processes are a class of continuous-time Markov process with almost surely continuous sample paths. Diffusion process is stochastic in nature and hence is used to model many real-life stochastic systems.
Since its first publication in 1965 in the series Grundlehren der mathematischen Wissenschaften this book has had a profound and enduring influence on research into the stochastic processes associated with diffusion phenomena.
1 sty 2014 · A diffusion process is a Markov process that has continuous sample paths (trajectories). Thus, it is a Markov process with no jumps. A diffusion process can be defined by specifying its first two moments together with the requirement that there be no jumps.
1 sty 2017 · The fundamental theories of diffusion and solid dissolution are reviewed in this chapter. Diffusion is a process by which small particles such as atoms and molecules are transported from a region of higher concentration to a region of lower concentration by random motion of the particles.
Basic concepts on stochastic processes. Let (Ω,A,P) be a common probability space and T the time set. A stochastic process X = {X. t , t ∈T } is a function X : T × Ω → R such that. X(t, . ) : Ω → R is a random variable for each t ∈T, X( . ,ω) : T → R is a sample path for each ω ∈ Ω.
Diffusion theory has a long and honorable place in population genetics theory, going back to Fisher (1922). In this chapter we consider the elements of the theory divorced from specific genetical applications, and in Chapter 5 the theory developed here will be applied to a variety of genetical models.
This is an appealing introduction to the theory of Markov processes with continuous sample paths, based on stochastic analysis by interpreting diffusion processes as solutions of Itô's Stochastic integral equation.
