Small random perturbations in second-order oscillatory systems

1992 ◽  
Vol 44 (1) ◽  
pp. 7-12
Author(s):  
O. V. Borisenko
Keyword(s):  
Second Order ◽  
Random Perturbations ◽  
Oscillatory Systems ◽  
Small Random Perturbations

scholarly journals Second-order differential equations with random perturbations and small parameters

2017 ◽  
Vol 147 (4) ◽  
pp. 763-779
Author(s):  
M. Kamenskii ◽  
S. Pergamenchtchikov ◽  
M. Quincampoix
Keyword(s):  
Differential Equations ◽  
Small Parameter ◽  
Random Perturbation ◽  
Stochastic Averaging ◽  
Second Order ◽  
Random Perturbations ◽  
Existence And Uniqueness Theorem ◽  
Second Order Differential Equations ◽  
Averaging Theorem ◽  
Small Parameters

We consider boundary-value problems for differential equations of second order containing a Brownian motion (random perturbation) and a small parameter and prove a special existence and uniqueness theorem for random solutions. We study the asymptotic behaviour of these solutions as the small parameter goes to zero and show the stochastic averaging theorem for such equations. We find the explicit limits for the solutions as the small parameter goes to zero.

Small random perturbations of peano phenomena

Stochastics ◽  
1982 ◽  
Vol 6 (3-4) ◽  
pp. 279-292 ◽  
Author(s):  
R. Bafico ◽  
P. Baldi
Keyword(s):  
Random Perturbations ◽  
Small Random Perturbations
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