To the maximum principle theory for problems of control of stochastic differential equations

2005 ◽  
pp. 255-263
Author(s):  
B. I. Arkin ◽  
M. T. Saksonov
Keyword(s):  
Maximum Principle ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
The Maximum Principle ◽  
Principle Theory

Phragmèn-Lindelöf and Comparison Theorems for Elliptic-Parabolic Differential Equations

1967 ◽  
Vol 19 ◽  
pp. 864-871
Author(s):  
J. K. Oddson
Keyword(s):  
Maximum Principle ◽  
Differential Equations ◽  
Parabolic Equations ◽  
Comparison Theorems ◽  
Parabolic Differential Equations ◽  
The Maximum Principle ◽  
Comparison Functions

Theorems of Phragmèn-Lindelöf type and other related results for solutions of elliptic-parabolic equations have been given by numerous authors in recent years. Many of these results are based upon the maximum principle and the use of auxiliary comparison functions which are constructed as supersolutions of the equations under various conditions on the coefficients. In this paper we present an axiomatized treatment of these topics, replacing specific hypotheses on the nature of the coefficients of the equations by a single assumption concerning the maximum principle and another concerning the existence of positive supersolutions, in terms of which the theorems are stated.

scholarly journals An optimal control of a risk-sensitive problem for backward doubly stochastic differential equations with applications

2020 ◽  
Vol 28 (1) ◽  
pp. 1-18
Author(s):  
Dahbia Hafayed ◽  
Adel Chala
Keyword(s):  
Differential Equation ◽  
Optimal Control ◽  
Maximum Principle ◽  
Differential Equations ◽  
Stochastic Differential Equation ◽  
Control Problem ◽  
Stochastic Differential Equations ◽  
Doubly Stochastic ◽  
Risk Sensitive ◽  
Performance Functional

AbstractIn this paper, we are concerned with an optimal control problem where the system is driven by a backward doubly stochastic differential equation with risk-sensitive performance functional. We generalized the result of Chala [A. Chala, Pontryagin’s risk-sensitive stochastic maximum principle for backward stochastic differential equations with application, Bull. Braz. Math. Soc. (N. S.) 48 2017, 3, 399–411] to a backward doubly stochastic differential equation by using the same contribution of Djehiche, Tembine and Tempone in [B. Djehiche, H. Tembine and R. Tempone, A stochastic maximum principle for risk-sensitive mean-field type control, IEEE Trans. Automat. Control 60 2015, 10, 2640–2649]. We use the risk-neutral model for which an optimal solution exists as a preliminary step. This is an extension of an initial control system in this type of problem, where an admissible controls set is convex. We establish necessary as well as sufficient optimality conditions for the risk-sensitive performance functional control problem. We illustrate the paper by giving two different examples for a linear quadratic system, and a numerical application as second example.

scholarly journals The maximum principle for a type of hereditary semilinear differential equation

1994 ◽  
Vol 36 (2) ◽  
pp. 194-212
Author(s):  
Feiyue He
Keyword(s):  
Differential Equation ◽  
Optimal Control ◽  
Maximum Principle ◽  
Differential Equations ◽  
Optimal Control Problem ◽  
Control Problem ◽  
The Maximum Principle ◽  
Semilinear Differential Equation

AbstractAn optimal control problem governed by a class of delay semilinear differential equations is studied. The existence of an optimal control is proven, and the maximum principle and approximating schemes are found. As applications, three examples are discussed.

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