scholarly journals The synchronization of coupled stochastic systems driven by symmetric α-stable process and Brownian motion

Filomat ◽  
2018 ◽  
Vol 32 (6) ◽  
pp. 2219-2245
Author(s):  
Shahad Al-Azzawi ◽  
Jicheng Liu ◽  
Xianming Liu
Keyword(s):  
Dynamical System ◽  
Mathematical Model ◽  
Brownian Motion ◽  
Gaussian Noise ◽  
Stochastic Systems ◽  
Stable Process ◽  
Symmetric Stable Process ◽  
And Brownian Motion ◽  
Coupled Dynamical System ◽  
Non Gaussian

The synchronization of stochastic differential equations (SDEs) driven by symmetric ?-stable process and Brownian Motion is investigated in pathwise sense. This coupled dynamical system is a new mathematical model, where one of the systems is driven by Gaussian noise, another one is driven by non- Gaussian noise. In this paper, we prove that the synchronization still persists for this coupled dynamical system. Examples and simulations are given.

scholarly journals On the Fractional Wave Equation

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 874
Author(s):  
Francesco Iafrate ◽  
Enzo Orsingher
Keyword(s):  
Brownian Motion ◽  
Wave Equation ◽  
Wave Equations ◽  
Stable Process ◽  
Space Time ◽  
Probabilistic Interpretation ◽  
Symmetric Stable Process ◽  
Fractional Wave Equation ◽  
Fractional Wave Equations ◽  
Time Fractional Wave Equation

In this paper we study the time-fractional wave equation of order 1 < ν < 2 and give a probabilistic interpretation of its solution. In the case 0 < ν < 1 , d = 1 , the solution can be interpreted as a time-changed Brownian motion, while for 1 < ν < 2 it coincides with the density of a symmetric stable process of order 2 / ν . We give here an interpretation of the fractional wave equation for d > 1 in terms of laws of stable d−dimensional processes. We give a hint at the case of a fractional wave equation for ν > 2 and also at space-time fractional wave equations.

scholarly journals Stability of stochastic systems with jumps

1996 ◽  
Vol 3 (2) ◽  
pp. 173-185 ◽  
Author(s):  
E. K. Boukas ◽  
H. Yang
Keyword(s):  
Brownian Motion ◽  
Control Strategy ◽  
State Feedback ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
And Brownian Motion ◽  
Quadratic Stabilization ◽  
Guaranteed Cost ◽  
Linear And Nonlinear Systems

This paper deals with stochastic stability of systems with Markovian jumps and Brownian motion. Mainly, we present sufficient conditions for quadratic stabilization of Ito type stochastic linear and nonlinear systems with Markovian jumps and Brownian motion using state feedback control. We also prove the guaranteed cost property of the proposed control strategy for the linear case.

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