Exact controllability of stochastic differential equations with memory

2020 ◽  
Vol 142 ◽  
pp. 104732
Author(s):  
Yanqing Wang ◽  
Xiuxiang Zhou
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Exact Controllability ◽  
With Memory

STATIONARY SOLUTIONS OF STOCHASTIC DIFFERENTIAL EQUATIONS WITH MEMORY AND STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS

2005 ◽  
Vol 07 (05) ◽  
pp. 553-582 ◽  
Author(s):  
YURI BAKHTIN ◽  
JONATHAN C. MATTINGLY
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Stationary Solution ◽  
Landau Equation ◽  
Stationary Solutions ◽  
Navier Stokes ◽  
Partial Differential ◽  
Navier Stokes Equation ◽  
With Memory

We explore Itô stochastic differential equations where the drift term possibly depends on the infinite past. Assuming the existence of a Lyapunov function, we prove the existence of a stationary solution assuming only minimal continuity of the coefficients. Uniqueness of the stationary solution is proven if the dependence on the past decays sufficiently fast. The results of this paper are then applied to stochastically forced dissipative partial differential equations such as the stochastic Navier–Stokes equation and stochastic Ginsburg–Landau equation.

scholarly journals Exact controllability of linear stochastic differential equations and related problems

2017 ◽  
Vol 7 (2) ◽  
pp. 305-345 ◽  
Author(s):  
Yanqing Wang ◽  
◽  
Donghui Yang ◽  
Jiongmin Yong ◽  
Zhiyong Yu ◽  
...  
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Exact Controllability

On the partial controllability of SDEs and the exact controllability of FBSDES

2020 ◽  
Vol 26 ◽  
pp. 68 ◽  
Author(s):  
Yanqing Wang ◽  
Zhiyong Yu
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Optimal Control Problems ◽  
Exact Controllability ◽  
Adjoint Equations ◽  
Control Problems ◽  
Output Controllability ◽  
Time Invariant ◽  
Partial Controllability

A notion of partial controllability (also can be called directional controllability or output controllability) is proposed for linear controlled (forward) stochastic differential equations (SDEs), which characterizes the ability of the state to reach some given random hyperplane. It generalizes the classical notion of exact controllability. For time-invariant system, checkable rank conditions ensuring SDEs’ partial controllability are provided. With some special setting, the partial controllability for SDEs is proved to be equivalent to the exact controllability for linear controlled forward-backward stochastic differential equations (FBSDEs). Moreover, we obtain some equivalent conclusions to partial controllability for SDEs or exact controllability for FBSDEs, including the validity of observability inequalities for the adjoint equations, the solvability of some optimal control problems, the solvability of norm optimal control problems, and the non-singularity of a random version of Gramian matrix.

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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