The exit path of a Markov chain with rare transitions
Olivier Catoni, Raphaël Cerf (1997)
ESAIM: Probability and Statistics
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Olivier Catoni, Raphaël Cerf (1997)
ESAIM: Probability and Statistics
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Rahim A. Abbaspour, Farhad Samadzadegan (2010)
Computer Science and Information Systems
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Olivier Catoni, Raphaël Cerf (2010)
ESAIM: Probability and Statistics
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We study the exit path from a general domain after the last visit to a set of a Markov chain with rare transitions. We prove several large deviation principles for the law of the succession of the cycles visited by the process (the cycle path), the succession of the saddle points gone through to jump from cycle to cycle on the cycle path (the saddle path) and the succession of all the points gone through (the exit path). We estimate the time the process spends in each cycle of...
Zbigniew Tarapata (2007)
International Journal of Applied Mathematics and Computer Science
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The paper presents selected multicriteria (multiobjective) approaches to shortest path problems. A classification of multi-objective shortest path (MOSP) problems is given. Different models of MOSP problems are discussed in detail. Methods of solving the formulated optimization problems are presented. An analysis of the complexity of the presented methods and ways of adapting of classical algorithms for solving multiobjective shortest path problems are described. A comparison of the...