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Perturbation Theory for Continuous Stochastic Equations
Author(s) -
Chechetkin V. R.,
Lutovinov V. S.
Publication year - 1987
Publication title -
fortschritte der physik/progress of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.2190351203
Subject(s) - multiplicative noise , non equilibrium thermodynamics , master equation , statistical physics , perturbation theory (quantum mechanics) , multiplicative function , perturbation (astronomy) , smoluchowski coagulation equation , mathematics , gaussian , birth–death process , stochastic process , phase transition , physics , mathematical analysis , quantum mechanics , computer science , population , statistics , demography , signal transfer function , digital signal processing , analog signal , sociology , computer hardware , quantum
The various general perturbational schemes for continuous stochastic equations are considered. These schemes have many analogous features with the iterational solution of Schwinger equation for S ‐matrix. The following problems are discussed: continuous stochastic evolution equations for probaibility distribution functionals, evolution equations for equal time correlators, perturbation theory for Gaussian and Poissonian additive noise, perturbation theory for birth and death processes. stochastic properties of systems with multiplicative noise. The general results are illustrated by diffusion ‐ controlled reactions, fluctuations in closed systems with chemical processes, propagation of waves in random media in parabolic equation approximation, and nonequilibrium phase transitions in systems with Poissonian breeding centers. The rate of irreversible reaction X + X → A (Smoluchowski process) is calculated with the use of general theory based on continuous stochastic equations for birth and death processes. The threshold criterion and range of fluctuational region for synergetic phase transition in system with Poissonian breeding centers are also considered.