Theory and applications of stochastic differential equations
Presents theory, sources, and applications of stochastic differential equations of Ito's type; those containing white noise. Closely studies first passage problems by modern singular perturbation methods and their role in various fields of science. Introduces analytical methods to obtain information on probabilistic quantities. Demonstrates the role of partial differential equations in this context. Clarifies the relationship between the complex mathematical theories involved and sources of the problem for physicists, chemists, engineers, and other non-mathematical specialists.
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Review of Probability Theory
The Brownian Motion
The Stochastic ltd Calculus
12 other sections not shown
approximation assume backward Kolmogorov equation boundary conditions boundary layer boundary value problem Brownian motion Brownian particle called collisions compute Consider constant construct converges coordinates cycle slips defined denote Derive determined deterministic diffusion coefficient diffusion process distribution domain dx(t eigenvalue elementary events elliptic equilibrium point example EXERCISE expected exit filter Find finite Fokker-Planck equation follows frequency Gaussian variable given Green's function hence independent inequality internal layer interval Ito's formula Langevin equation lattice layer expansion leading term Liouville's Markov mathematical matrix modulation molecules nonanticipating normal obtain one-dimensional partial differential equations phase space potential barrier properties random events random variable random walk reaction rate saddle points sample space satisfies Schuss Section sequence Show Smoluchowski smooth function solution stochastic differential equation stochastic integral Stratonovich Stratonovich integral subsets theorem theory tion tosses trajectories transition probability density ue(x vector velocity white noise zero
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