Physics Today · 1981 · 508 citations · 0 references
Natural SciencesMathematicsPhysicsDifferential EquationsProbability TheoryStochastic ProcessesDiffusion ProcessesPartial Differential EquationsPerturbation MethodsSingular Perturbation TheoryStochastic CalculusStochastic Differential EquationsFirst-passage ProblemsItô CalculusNonlinear Partial Differential EquationsSingular Perturbation AnalysisStochastic Differential SystemsStochastic IntegralsStochastic Partial Differential EquationsWhite Noise
The paper surveys Ito-type stochastic differential equations, covering their theory, sources, and applications. The study introduces analytical methods for extracting probabilistic information. It employs modern singular perturbation techniques to analyze first‑passage problems across scientific disciplines. The work shows how partial differential equations underpin the theory and clarifies their relevance to physicists, chemists, engineers, and other specialists.
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.