Multi-valued stochastic differential equations driven byG-Brownian motion and related stochastic control problems

2016 ◽  
Vol 90 (5) ◽  
pp. 1132-1154 ◽  
Author(s):  
Yong Ren ◽  
Jun Wang ◽  
Lanying Hu
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Stochastic Control ◽  
Control Problems ◽  
Stochastic Control Problems

scholarly journals Stochastic Optimization Theory of Backward Stochastic Differential Equations Driven by G-Brownian Motion

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Zhonghao Zheng ◽  
Xiuchun Bi ◽  
Shuguang Zhang
Keyword(s):  
Optimal Control ◽  
Brownian Motion ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Stochastic Optimal Control ◽  
Optimal Control Problems ◽  
Backward Stochastic Differential Equations ◽  
Dynamic Programming Principle ◽  
Control Problems ◽  
Order Partial Differential Equation

We consider the stochastic optimal control problems under G-expectation. Based on the theory of backward stochastic differential equations driven by G-Brownian motion, which was introduced in Hu et al. (2012), we can investigate the more general stochastic optimal control problems under G-expectation than that were constructed in Zhang (2011). Then we obtain a generalized dynamic programming principle, and the value function is proved to be a viscosity solution of a fully nonlinear second-order partial differential equation.

An Optimal Treatment Strategy for Diabetes

2003 ◽  
Vol 11 (04) ◽  
pp. 419-425 ◽  
Author(s):  
Farai Nyabadza ◽  
Edward M. Lungu
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Control Problem ◽  
Stochastic Differential Equations ◽  
Stochastic Control ◽  
Treatment Strategy ◽  
Sufficient Conditions ◽  
Optimal Treatment ◽  
The Body ◽  
Optimal Treatment Strategy

Consider a system on n variables involved in the regulation of glucose in the body, whose concentrations are given by stochastic differential equations driven by m-dimensional Brownian motion. We formulate a stochastic control problem and give sufficient conditions for the existence of an optimal treatment strategy. We study the following problem: what treatment strategy for the n variables, maximizes the expected benefit from treatment.

scholarly journals Stabilization of Stochastic Differential Equations Driven by G-Brownian Motion with Aperiodically Intermittent Control

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 988
Author(s):  
Pengju Duan
Keyword(s):  
Brownian Motion ◽  
Lyapunov Function ◽  
Differential Equations ◽  
Exponential Stability ◽  
Stochastic Differential Equations ◽  
Mild Solution ◽  
Intermittent Control

The paper is devoted to studying the exponential stability of a mild solution of stochastic differential equations driven by G-Brownian motion with an aperiodically intermittent control. The aperiodically intermittent control is added into the drift coefficients, when intermittent intervals and coefficients satisfy suitable conditions; by use of the G-Lyapunov function, the p-th exponential stability is obtained. Finally, an example is given to illustrate the availability of the obtained results.

Moderate deviation principle for multivalued stochastic differential equations

2019 ◽  
Vol 20 (03) ◽  
pp. 2050015 ◽  
Author(s):  
Hua Zhang
Keyword(s):  
Brownian Motion ◽  
Weak Convergence ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Moderate Deviation ◽  
Reflected Brownian Motion ◽  
Moderate Deviation Principle ◽  
Deviation Principle ◽  
Weak Convergence Approach

In this paper, we prove a moderate deviation principle for the multivalued stochastic differential equations whose proof are based on recently well-developed weak convergence approach. As an application, we obtain the moderate deviation principle for reflected Brownian motion.

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