scholarly journals Weak Second Order Multirevolution Composition Methods for Highly Oscillatory Stochastic Differential Equations with Additive or Multiplicative Noise

2014 ◽  
Vol 36 (4) ◽  
pp. A1770-A1796 ◽  
Author(s):  
Gilles Vilmart
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Multiplicative Noise ◽  
Second Order ◽  
Composition Methods ◽  
Highly Oscillatory

Numerical Integration of Multiplicative-Noise Stochastic Differential Equations

1985 ◽  
Vol 22 (6) ◽  
pp. 1153-1166 ◽  
Author(s):  
John R. Klauder ◽  
Wesley P. Petersen
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Numerical Integration ◽  
Multiplicative Noise

Asymptotic stability of second-order neutral stochastic differential equations

2010 ◽  
Vol 51 (5) ◽  
pp. 052701 ◽  
Author(s):  
R. Sakthivel ◽  
Yong Ren ◽  
Hyunsoo Kim
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Second Order

Asymptotic-numerical solvers for highly oscillatory second-order differential equations

2019 ◽  
Vol 137 ◽  
pp. 184-202
Author(s):  
Zhongli Liu ◽  
Tianhai Tian ◽  
Hongjiong Tian
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Second Order Differential Equations ◽  
Highly Oscillatory

A variational approach to nonlinear stochastic differential equations with linear multiplicative noise

2019 ◽  
Vol 25 ◽  
pp. 71
Author(s):  
Viorel Barbu
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Parabolic Equations ◽  
Optimization Problem ◽  
Multiplicative Noise ◽  
Generalized Solution ◽  
Convex Optimization Problem ◽  
Nonlinear Stochastic Differential Equations ◽  
Infinite Dimensional ◽  
Wiener Processes

One introduces a new concept of generalized solution for nonlinear infinite dimensional stochastic differential equations of subgradient type driven by linear multiplicative Wiener processes. This is defined as solution of a stochastic convex optimization problem derived from the Brezis-Ekeland variational principle. Under specific conditions on nonlinearity, one proves the existence and uniqueness of a variational solution which is also a strong solution in some significant situations. Applications to the existence of stochastic total variational flow and to stochastic parabolic equations with mild nonlinearity are given.

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