Explicit Integration of Stiff Stochastic Differential Equations via an Efficient Implementation of Stochastic Computational Singular Perturbation

2019 ◽  
Vol 25 (5) ◽  
Author(s):  
Lijin Wang ◽  
Yanzhao Cao ◽  
Sau-Hai Lam
Keyword(s):  
Differential Equations ◽  
Singular Perturbation ◽  
Stochastic Differential Equations ◽  
Efficient Implementation ◽  
Explicit Integration ◽  
Computational Singular Perturbation

scholarly journals Symmetry Analysis of the Stochastic Logistic Equation

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 973
Author(s):  
Giuseppe Gaeta
Keyword(s):  
General Theory ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Explicit Formula ◽  
Logistic Equation ◽  
Noise Amplitude ◽  
Constant Amplitude ◽  
Complete Model ◽  
Explicit Integration ◽  
Single Realization

We apply the recently developed theory of symmetry of stochastic differential equations to stochastic versions of the logistic equation; these may have environmental or demographical noise, or both—in which case we speak of the complete model. We study all these cases, both with constant and with non-constant noise amplitude, and show that the only one in which there are nontrivial symmetries is that of the stochastic logistic equation with (constant amplitude) environmental noise. In this case, the general theory of symmetry of stochastic differential equations is used to obtain an explicit integration, i.e., an explicit formula for the process in terms of any single realization of the driving Wiener process.

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
Sign in / Sign up

Export Citation Format

Share Document