Nonlinear parabolic stochastic differential equations with additive colored noise onR d �R +: A regulated stochastic quantization

1987 ◽  
Vol 109 (4) ◽  
pp. 537-561 ◽  
Author(s):  
Charles R. Doering
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Colored Noise ◽  
Stochastic Quantization ◽  
Nonlinear Parabolic

scholarly journals Investigation of high order stochastic differential equations using averaging method

2007 ◽  
Vol 29 (3) ◽  
pp. 249-255
Author(s):  
Nguyen Dong Anh ◽  
Ngo Thi Hong Hue
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Nonlinear Oscillation ◽  
Colored Noise ◽  
Averaging Method ◽  
Nonlinear Oscillations ◽  
High Order ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Stochastic Problems

The averaging method is a useful tool for investigating both deterministic and stochastic quasilinear system. In the stochastic problems, however, the method has often been developed only for mechanical systems subjected to white noise excitations.In the paper this method is applied to high order stochastic differential equations. The nonlinear oscillations in high order deterministic differential equations were investigated in the fundamental work of Prof. Nguyen Van Dao. As an application of high order stochastic differential equations the nonlinear oscillation of single degree of freedom systems subjected to the excitation of a class of colored noises is outlined. The results obtained show that the higher order averaging method can also be successfully extended to the cases of colored noise excitation.

Stability of Implicit Difference Equations Generated by Parabolic Functional Differential Problems

2007 ◽  
Vol 7 (1) ◽  
pp. 68-82
Author(s):  
K. Kropielnicka
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Initial Boundary ◽  
Numerical Examples ◽  
Convergence Results ◽  
Nonlinear Parabolic ◽  
Implicit Difference Methods ◽  
Neumann Type ◽  
Difference Methods ◽  
Functional Differential

AbstractA general class of implicit difference methods for nonlinear parabolic functional differential equations with initial boundary conditions of the Neumann type is constructed. Convergence results are proved by means of consistency and stability arguments. It is assumed that given functions satisfy nonlinear estimates of Perron type with respect to functional variables. Differential equations with deviated variables and differential integral problems can be obtained from a general model by specializing given operators. The results are illustrated by numerical examples.

Stochastic Differential Equations for Power Law Behaviors

2012 ◽  
Author(s):  
Bo Jiang ◽  
Roger Brockett ◽  
Weibo Gong ◽  
Don Towsley
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Power Law
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