Optimal Stabilization of Families of Linear Stochastic Differential Equations with Jump Coefficients and Multiplicative Noise

1987 ◽  
Vol 25 (6) ◽  
pp. 1587-1600 ◽  
Author(s):  
William E. Hopkins, Jr.
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Multiplicative Noise ◽  
Optimal Stabilization

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

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.

A family of fully implicit Milstein methods for stiff stochastic differential equations with multiplicative noise

2012 ◽  
Vol 52 (3) ◽  
pp. 741-772 ◽  
Author(s):  
Xiaojie Wang ◽  
Siqing Gan ◽  
Desheng Wang
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Multiplicative Noise ◽  
Fully Implicit

Fast Numerical Integrator for Stochastic Differential Equations with Nonstationary Multiplicative Noise†

2001 ◽  
Vol 105 (12) ◽  
pp. 2687-2693 ◽  
Author(s):  
Eli Hershkovitz ◽  
Rigoberto Hernandez
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Multiplicative Noise ◽  
Numerical Integrator
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