Simulated annealing process in general state space

1991 ◽  
Vol 23 (4) ◽  
pp. 866-893 ◽  
Author(s):  
Heikki Haario ◽  
Eero Saksman
Keyword(s):  
Stochastic Process ◽  
Simulated Annealing ◽  
State Space ◽  
Annealing Process ◽  
General State ◽  
Arbitrary State ◽  
Strong And Weak Convergence ◽  
General State Space ◽  
Rate Of Cooling ◽  
Space Conditions

The stochastic process corresponding to the simulated annealing optimization algorithm is generalized to the case of an arbitrary state space. Conditions for the strong and weak convergence of the process are established. In addition the relation between the size of the generating distributions and the possible rate of cooling is studied.

Simulated annealing process in general state space

1991 ◽  
Vol 23 (04) ◽  
pp. 866-893 ◽  
Author(s):  
Heikki Haario ◽  
Eero Saksman
Keyword(s):  
Stochastic Process ◽  
Simulated Annealing ◽  
State Space ◽  
Annealing Process ◽  
General State ◽  
Arbitrary State ◽  
Strong And Weak Convergence ◽  
General State Space ◽  
Rate Of Cooling ◽  
Space Conditions

The stochastic process corresponding to the simulated annealing optimization algorithm is generalized to the case of an arbitrary state space. Conditions for the strong and weak convergence of the process are established. In addition the relation between the size of the generating distributions and the possible rate of cooling is studied.

Criteria for classifying general Markov chains

1976 ◽  
Vol 8 (04) ◽  
pp. 737-771 ◽  
Author(s):  
R. L. Tweedie
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
State Space ◽  
The State ◽  
General State ◽  
Classical Work ◽  
The Status ◽  
General State Space

The aim of this paper is to present a comprehensive set of criteria for classifying as recurrent, transient, null or positive the sets visited by a general state space Markov chain. When the chain is irreducible in some sense, these then provide criteria for classifying the chain itself, provided the sets considered actually reflect the status of the chain as a whole. The first part of the paper is concerned with the connections between various definitions of recurrence, transience, nullity and positivity for sets and for irreducible chains; here we also elaborate the idea of status sets for irreducible chains. In the second part we give our criteria for classifying sets. When the state space is countable, our results for recurrence, transience and positivity reduce to the classical work of Foster (1953); for continuous-valued chains they extend results of Lamperti (1960), (1963); for general spaces the positivity and recurrence criteria strengthen those of Tweedie (1975b).

Reversibility of Markov chains with applications to storage models

1985 ◽  
Vol 22 (01) ◽  
pp. 123-137 ◽  
Author(s):  
Hideo Ōsawa
Keyword(s):  
Markov Chains ◽  
State Space ◽  
Discrete Time ◽  
Risk Model ◽  
Sufficient Conditions ◽  
Single Server ◽  
General State ◽  
Insurance Risk ◽  
General State Space ◽  
Necessary And Sufficient

This paper studies the reversibility conditions of stationary Markov chains (discrete-time Markov processes) with general state space. In particular, we investigate the Markov chains having atomic points in the state space. Such processes are often seen in storage models, for example waiting time in a queue, insurance risk reserve, dam content and so on. The necessary and sufficient conditions for reversibility of these processes are obtained. Further, we apply these conditions to some storage models and present some interesting results for single-server queues and a finite insurance risk model.

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