On Gaussian approximation of Hilbert space valued discrete time martingales

1993 ◽  
Vol 33 (4) ◽  
pp. 368-380 ◽  
Author(s):  
A. Raĉkauskas
Keyword(s):  
Hilbert Space ◽  
Discrete Time ◽  
Gaussian Approximation

scholarly journals Lyapunov Type Theorems for Exponential Stability of Linear Skew-Product Three-Parameter Semiflows with Discrete Time

Axioms ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 47 ◽  
Author(s):  
Davor Dragičević ◽  
Ciprian Preda
Keyword(s):  
Hilbert Space ◽  
Exponential Stability ◽  
Discrete Time ◽  
Lyapunov Functions ◽  
Complete Characterization ◽  
Skew Product ◽  
Linear Perturbations

For linear skew-product three-parameter semiflows with discrete time acting on an arbitrary Hilbert space, we obtain a complete characterization of exponential stability in terms of the existence of appropriate Lyapunov functions. As a nontrivial application of our work, we prove that the notion of an exponential stability persists under sufficiently small linear perturbations.

Statevector reduction in discrete time: A random walk in Hilbert space

1994 ◽  
Vol 24 (3) ◽  
pp. 363-377 ◽  
Author(s):  
Akihiro Nakano ◽  
Philip Pearle
Keyword(s):  
Hilbert Space ◽  
Random Walk ◽  
Discrete Time

On a discrete-time version of a problem of A. J. Pritchard and J. Zabczyk

1985 ◽  
Vol 101 (1-2) ◽  
pp. 159-161 ◽  
Author(s):  
K. Maciej Przyłuski
Keyword(s):  
Hilbert Space ◽  
Discrete Time ◽  
Bounded Operator ◽  
Linear Operators ◽  
Discrete Time System ◽  
Bounded Linear Operators ◽  
Time System ◽  
Bounded Linear ◽  
Strongly Continuous Semigroups ◽  
Stable Linear

SynopsisIt is shown that every weakly l1-stable linear and bounded operator (which represents a linear discrete-time system) on a Hilbert space is power stable. It solves (at least partially) a discrete-time version of a problem posed by A. J. Pritchard and J. Zabczyk for strongly continuous semigroups of bounded linear operators.

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