A bound for the distribution of a stopping time for a stochastic system

1996 ◽  
Vol 37 (4) ◽  
pp. 683-689 ◽  
Author(s):  
K. A. Borovkov
Keyword(s):  
Stochastic System ◽  
Stopping Time

Products of 2 × 2 stochastic matrices with random entries

1986 ◽  
Vol 23 (04) ◽  
pp. 1019-1024
Author(s):  
Walter Van Assche
Keyword(s):  
Rate Of Convergence ◽  
Beta Distribution ◽  
Stopping Time ◽  
Stochastic Matrices

The limit of a product of independent 2 × 2 stochastic matrices is given when the entries of the first column are independent and have the same symmetric beta distribution. The rate of convergence is considered by introducing a stopping time for which asymptotics are given.

Multiple Models Direct Adaptive Decoupling Controller for a Stochastic System

2010 ◽  
Vol 36 (9) ◽  
pp. 1295-1304 ◽  
Author(s):  
Yi-Hui ZHENG ◽  
Xin WANG ◽  
Shao-Yuan LI ◽  
Jian-Guo JIANG
Keyword(s):  
Stochastic System ◽  
Multiple Models

Optimal Stopping Time for Geometric Random Walks with Power Payoff Function

2020 ◽  
Vol 81 (7) ◽  
pp. 1192-1210
Author(s):  
O.V. Zverev ◽  
V.M. Khametov ◽  
E.A. Shelemekh
Keyword(s):  
Random Walks ◽  
Optimal Stopping ◽  
Stopping Time ◽  
Payoff Function ◽  
Optimal Stopping Time

Simplified analysis of a stochastic system

1979 ◽  
Vol 44 (2) ◽  
pp. 328-339
Author(s):  
Vladimír Herles
Keyword(s):  
Statistical Analysis ◽  
Dynamic Behavior ◽  
Stochastic System ◽  
Additive Noise ◽  
Random Parameter ◽  
Systematic Difference ◽  
Order System ◽  
Constant Parameter ◽  
Random Parameters ◽  
Simplified Analysis

Contradictious results published by different authors about the dynamics of systems with random parameters have been examined. Statistical analysis of the simple 1st order system proves that the random parameter can cause a systematic difference in the dynamic behavior that cannot be (in general) described by the usual constant-parameter model with the additive noise at the output.

scholarly journals A Type of Time-Symmetric Stochastic System and Related Games

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 118
Author(s):  
Qingfeng Zhu ◽  
Yufeng Shi ◽  
Jiaqiang Wen ◽  
Hui Zhang
Keyword(s):  
Nash Equilibrium ◽  
Time Delay ◽  
Differential Equations ◽  
Equilibrium Point ◽  
Stochastic Differential Equations ◽  
Stochastic System ◽  
Stochastic Systems ◽  
Necessary Condition ◽  
Nash Equilibrium Point ◽  
Doubly Stochastic

This paper is concerned with a type of time-symmetric stochastic system, namely the so-called forward–backward doubly stochastic differential equations (FBDSDEs), in which the forward equations are delayed doubly stochastic differential equations (SDEs) and the backward equations are anticipated backward doubly SDEs. Under some monotonicity assumptions, the existence and uniqueness of measurable solutions to FBDSDEs are obtained. The future development of many processes depends on both their current state and historical state, and these processes can usually be represented by stochastic differential systems with time delay. Therefore, a class of nonzero sum differential game for doubly stochastic systems with time delay is studied in this paper. A necessary condition for the open-loop Nash equilibrium point of the Pontriagin-type maximum principle are established, and a sufficient condition for the Nash equilibrium point is obtained. Furthermore, the above results are applied to the study of nonzero sum differential games for linear quadratic backward doubly stochastic systems with delay. Based on the solution of FBDSDEs, an explicit expression of Nash equilibrium points for such game problems is established.

scholarly journals Almost conservation laws for stochastic nonlinear Schrödinger equations

2021 ◽  
Author(s):  
Kelvin Cheung ◽  
Guopeng Li ◽  
Tadahiro Oh
Keyword(s):  
Conservation Laws ◽  
Stopping Time ◽  
Energy Space ◽  
Stochastic Forcing ◽  
Time Dynamics ◽  
Nonlinear Schrödinger ◽  
Time Argument ◽  
Cubic Nonlinear Schrödinger Equation ◽  
Stochastic Setting ◽  
Ito's Lemma

AbstractIn this paper, we present a globalization argument for stochastic nonlinear dispersive PDEs with additive noises by adapting the I-method (= the method of almost conservation laws) to the stochastic setting. As a model example, we consider the defocusing stochastic cubic nonlinear Schrödinger equation (SNLS) on $${\mathbb {R}}^3$$ R 3 with additive stochastic forcing, white in time and correlated in space, such that the noise lies below the energy space. By combining the I-method with Ito’s lemma and a stopping time argument, we construct global-in-time dynamics for SNLS below the energy space.

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