Studies in nonlinear stochastic processes. III. Approximate solutions of nonlinear stochastic differential equations excited by Gaussian noise and harmonic disturbances

1977 ◽  
Vol 17 (1) ◽  
pp. 21-44 ◽  
Author(s):  
Aaron B. Budgor
Keyword(s):  
Differential Equations ◽  
Stochastic Processes ◽  
Stochastic Differential Equations ◽  
Gaussian Noise ◽  
Approximate Solutions ◽  
Nonlinear Stochastic Differential Equations

EXPANSION THEOREMS FOR GENERALIZED RANDOM PROCESSES, WICK PRODUCTS AND APPLICATIONS TO STOCHASTIC DIFFERENTIAL EQUATIONS

2007 ◽  
Vol 10 (01) ◽  
pp. 79-110 ◽  
Author(s):  
STEVAN PILIPOVIĆ ◽  
DORA SELEŠI
Keyword(s):  
Differential Equations ◽  
Stochastic Processes ◽  
Stochastic Differential Equations ◽  
Series Expansion ◽  
Random Processes ◽  
Wick Product ◽  
Nonlinear Stochastic Differential Equations ◽  
Wick Products

A new Gel'fand triple exp (S)1 ⊆ (L)2 ⊆ exp (S)-1 is constructed as extension of the known Kondratiev one (S)1 ⊆ (L)2 ⊆ (S)-1. Expansion theorems for generalized stochastic processes considered as elements of the spaces [Formula: see text] and [Formula: see text] are derived. This series expansion is used for solving a class of evolution stochastic differential equations. The Wick product is developed on the spaces exp (S)-1, [Formula: see text] and [Formula: see text]. The series expansion of generalized stochastic processes is used for solving a class of nonlinear stochastic differential equations by means of Wick products.

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