scholarly journals Existence-uniqueness and exponential estimate of pathwise solutions of retarded stochastic evolution systems with time smooth diffusion coefficients

2017 ◽  
Vol 37 (4) ◽  
pp. 2161-2180 ◽  
Author(s):  
Daoyi Xu ◽  
◽  
Weisong Zhou ◽  
Keyword(s):  
Diffusion Coefficients ◽  
Exponential Estimate ◽  
Stochastic Evolution ◽  
Pathwise Solutions ◽  
Evolution Systems

Boundary Control of Slender Beams Under Deterministic and Stochastic Loads

2017 ◽  
Vol 139 (9) ◽  
Author(s):  
K. D. Do
Keyword(s):  
Equations Of Motion ◽  
Type Theorem ◽  
Control Design ◽  
Well Posedness ◽  
Stochastic Evolution ◽  
Feedback Controllers ◽  
Slender Beams ◽  
Stochastic Loads ◽  
External Loads ◽  
Evolution Systems

This paper first derives equations of motion of extensible and shearable slender beams with large motions under both deterministic and stochastic external loads. Boundary feedback controllers are then proposed to achieve almost surely globally practically asymptotic stability. The control design, well-posedness, and stability analysis are based on a Lyapunov-type theorem developed for a class of stochastic evolution systems (SESs) in Hilbert space.

Adaptive control of linear stochastic evolution systems

1991 ◽  
Vol 36 (2) ◽  
pp. 71-90 ◽  
Author(s):  
T. E. Duncan ◽  
B. Pasik-duncan ◽  
B. Goldys
Keyword(s):  
Adaptive Control ◽  
Stochastic Evolution ◽  
Evolution Systems

Stochastic Evolution Systems

2018 ◽  
Author(s):  
Boris L. Rozovsky ◽  
Sergey V. Lototsky
Keyword(s):  
Stochastic Evolution ◽  
Evolution Systems

scholarly journals Existence and uniqueness of solutions for two- dimensional fractional non- colliding particle systems

2020 ◽  
Vol 71 (1) ◽  
pp. 11-17
Author(s):  
Huong Vu Thi
Keyword(s):  
Diffusion Coefficients ◽  
Existence And Uniqueness ◽  
Particle Systems ◽  
Electrostatic Repulsion ◽  
Nearest Neighbour ◽  
Two Dimensional ◽  
Stochastic Evolution ◽  
Uniqueness Of Solutions ◽  
Restoring Force ◽  
Brownian Particles

In this paper, we consider the stochastic evolution of two particles with electrostatic repulsion and restoring force which is modeled by a system of stochastic differential equations driven by fractional Brownian motion where the diffusion coefficients are constant. This is the simplest case for some classes of non- colliding particle systems such as Dyson Brownian motions, Brownian particles systems with nearest neighbour repulsion. We will prove that the equation has a unique non- colliding solution in path- wise sense.

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