scholarly journals Causality and stochastic realization

2005 ◽  
Vol 2005 (3) ◽  
pp. 349-356 ◽  
Author(s):  
Ljiljana Petrovic
Keyword(s):  
Hilbert Spaces ◽  
Realization Problem ◽  
Amount Of Information ◽  
Stochastic Realization

We consider a problem (that follows directly from realization problem) on finding Markovian representations for a given family of Hilbert spaces such that each of these two families provides exactly the same amount of information about some other family of Hilbert spaces.

On the nonlinear stochastic realization problem

1989 ◽  
Vol 26 (2) ◽  
pp. 65-79 ◽  
Author(s):  
T. J. S. Tayor ◽  
M. Pavon
Keyword(s):  
Realization Problem ◽  
Stochastic Realization

scholarly journals Some causal connections between stochastic dynamic systems

Filomat ◽  
2013 ◽  
Vol 27 (5) ◽  
pp. 865-873
Author(s):  
Ljiljana Petrovic
Keyword(s):  
Dynamic System ◽  
Hilbert Spaces ◽  
Dynamic Systems ◽  
Stochastic Dynamic ◽  
Realization Problem ◽  
Stochastic Dynamic System ◽  
Causal Connections ◽  
Causality Relationship ◽  
Stochastic Dynamic Systems

In this paper we consider a problem that follows directly from realization problem: how to find Markovian representations , even minimall, for a given family of Hilbert spaces, understood as outputs of a stochastic dynamic system S1, provided it is in a certain causality relationship with another family of Hilbert spaces , i. e. with some informations about states of a stochastic dynamic system S2. This paper is continuation of the papers Gill and Petrovic [7] and Petrovic [16,17].

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