scholarly journals Sufficient Stochastic Maximum Principle for Discounted Control Problem

2014 ◽  
Vol 70 (2) ◽  
pp. 225-252 ◽  
Author(s):  
Bohdan Maslowski ◽  
Petr Veverka
Keyword(s):  
Maximum Principle ◽  
Control Problem ◽  
Stochastic Maximum Principle ◽  
Discounted Control Problem

Malliavin calculus used to derive a stochastic maximum principle for system driven by fractional Brownian and standard Wiener motions with application

2020 ◽  
Vol 28 (4) ◽  
pp. 291-306
Author(s):  
Tayeb Bouaziz ◽  
Adel Chala
Keyword(s):  
Brownian Motion ◽  
Maximum Principle ◽  
Control Problem ◽  
Fractional Brownian Motion ◽  
Stochastic Control ◽  
Malliavin Calculus ◽  
Stochastic Maximum Principle ◽  
Hurst Parameter ◽  
Principle Of Optimality ◽  
Initial Cost

AbstractWe consider a stochastic control problem in the case where the set of the control domain is convex, and the system is governed by fractional Brownian motion with Hurst parameter {H\in(\frac{1}{2},1)} and standard Wiener motion. The criterion to be minimized is in the general form, with initial cost. We derive a stochastic maximum principle of optimality by using two famous approaches. The first one is the Doss–Sussmann transformation and the second one is the Malliavin derivative.

scholarly journals A Stochastic Maximum Principle for Control Problems Constrained by the Stochastic Navier–Stokes Equations

2021 ◽  
Author(s):  
Peter Benner ◽  
Christoph Trautwein
Keyword(s):  
Maximum Principle ◽  
Control Problem ◽  
Optimality Condition ◽  
Stokes Equations ◽  
Stochastic Maximum Principle ◽  
Navier Stokes ◽  
Control Problems ◽  
Optimal Controls ◽  
Sufficient Optimality Condition ◽  
Navier Stokes Equations

AbstractWe analyze the control problem of the stochastic Navier–Stokes equations in multi-dimensional domains considered in Benner and Trautwein (Math Nachr 292(7):1444–1461, 2019) restricted to noise terms defined by a Q-Wiener process. The cost functional related to this control problem is nonconvex. Using a stochastic maximum principle, we derive a necessary optimality condition to obtain explicit formulas the optimal controls have to satisfy. Moreover, we show that the optimal controls satisfy a sufficient optimality condition. As a consequence, we are able to solve uniquely control problems constrained by the stochastic Navier–Stokes equations especially for two-dimensional as well as for three-dimensional domains.

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