Open AccessFixed points and stability of A class of Stochastic dynamical system driven by Brownian motion
Author(s) -
Chunsheng Wang,
Hong Ding,
Tong Ouyang
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/2087/1/012052
Subject(s) - brownian motion , fixed point , mathematics , class (philosophy) , stability theory , stability (learning theory) , mean square , dynamical systems theory , square (algebra) , type (biology) , geometric brownian motion , zero (linguistics) , motion (physics) , statistical physics , mathematical economics , mathematical analysis , computer science , diffusion process , physics , statistics , nonlinear system , geometry , artificial intelligence , philosophy , quantum mechanics , machine learning , biology , ecology , knowledge management , innovation diffusion , linguistics
In real life, many models and systems are affected by random phenomena. For this reason, experts and scholars propose to describe these stochastic processes with Brownian motion respectively. In this paper we consider a kind of stochastic Vollterra dynamical systems of nonconvolution type and give some new conditions to ensure that the zero solution is asymptotically stable in mean square by means of fixed point method. The theorems of asymptotically stability in mean square with a necessary conditions are proved. Some results of related papers are improved.