Markov Processes on Infinite Dimensional Spaces, Markov Fields and Markov Cosurfaces

1985 ◽  
pp. 11-40 ◽  
Author(s):  
S. Albeverio ◽  
R. Høegh-Krohn ◽  
H. Holden
Keyword(s):  
Markov Processes ◽  
Infinite Dimensional ◽  
Markov Fields

scholarly journals QUANTUM MARKOV FIELDS

2003 ◽  
Vol 06 (01) ◽  
pp. 123-138 ◽  
Author(s):  
LUIGI ACCARDI ◽  
FRANCESCO FIDALEO
Keyword(s):  
Boundary Condition ◽  
Phase Transitions ◽  
Symmetry Breaking ◽  
Markov Processes ◽  
Markov Property ◽  
Lattice Systems ◽  
Conditional Expectations ◽  
Markov Fields ◽  
Quantum Lattice Systems ◽  
Quantum Markov Processes

The Markov property for quantum lattice systems is investigated in terms of generalized conditional expectations. General properties of (particular cases of) quantum Markov fields, i.e. quantum Markov processes with multi-dimensional indices, are pointed out. In such a way, deep connections with the KMS boundary condition, as well as phenomena of phase transitions and symmetry breaking, naturally emerge.

Dirichlet forms on partial *-algebras

1988 ◽  
Vol 104 (1) ◽  
pp. 129-140 ◽  
Author(s):  
G. O. S. Ekhaguere
Keyword(s):  
Markov Processes ◽  
Dirichlet Form ◽  
Dirichlet Forms ◽  
Function Spaces ◽  
Hunt Process ◽  
Partial Algebras ◽  
Markov Fields ◽  
Associated Function ◽  
Number Of Authors

Dirichlet forms and their associated function spaces have been studied by a number of authors [4, 6, 7, 12, 15–18, 22, 25, 26]. Important motivation for the study has been the connection of Dirichlet forms with Markov processes [16–18, 25, 26]: for example, to every regular symmetric Dirichlet form, there is an associated Hunt process [13, 20]. This makes the theory of Dirichlet forms a convenient source of examples of Hunt processes. In the non-commutative setting, Markov fields have been studied by several authors [1–3, 14, 19, 24, 28]. It is therefore interesting to develop a non-commutative extension of the theory of Dirichlet forms and to study their connection with non-commutative Markov processes.

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