Linearization of controlled stochastic evolution systems in a Hilbert space

1990 ◽  
Vol 42 (4) ◽  
pp. 467-471
Author(s):  
S. A. Mel'nik
Keyword(s):  
Hilbert Space ◽  
Stochastic Evolution ◽  
Evolution Systems

scholarly journals Controllability of semilinear stochastic evolution equations in Hilbert space

2001 ◽  
Vol 14 (4) ◽  
pp. 329-339 ◽  
Author(s):  
P. Balasubramaniam ◽  
J. P. Dauer
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Hilbert Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Evolution Equations ◽  
Stochastic Partial Differential Equation ◽  
Semigroup Theory ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations

Controllability of semilinear stochastic evolution equations is studied by using stochastic versions of the well-known fixed point theorem and semigroup theory. An application to a stochastic partial differential equation is given.

scholarly journals Large deviations for SPDEs of jump type

2015 ◽  
Vol 15 (04) ◽  
pp. 1550026 ◽  
Author(s):  
Xue Yang ◽  
Jianliang Zhai ◽  
Tusheng Zhang
Keyword(s):  
Hilbert Space ◽  
Weak Convergence ◽  
Evolution Equation ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Stochastic Evolution Equation ◽  
Stochastic Evolution ◽  
Random Measures ◽  
Convergence Method ◽  
Weak Convergence Method

In this paper, we establish a large deviation principle for a fully nonlinear stochastic evolution equation driven by both Brownian motions and Poisson random measures on a given Hilbert space H. The weak convergence method plays an important role.

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