For a general multidimensional denumerable state Markov process with any initial state probability vector, the probability density function and its LS transform of the first passage time to a certain given state set a...For a general multidimensional denumerable state Markov process with any initial state probability vector, the probability density function and its LS transform of the first passage time to a certain given state set are obtained and the algorithms for them are derived. It is proved that the resulting errors of the algorithms are both uniform in their respective arguments.Some numerical results are presented.展开更多
Let {(Xi, Si, μi) : i ℃ N} be a sequence of probability measure spaces and (*Xi, L(*Si), L(*μi)) be the Loeb measure space with respect to (Xi, Si, μi) for i ℃ N. Let X =× Xi, S = ×Si,μ = ×μi. We...Let {(Xi, Si, μi) : i ℃ N} be a sequence of probability measure spaces and (*Xi, L(*Si), L(*μi)) be the Loeb measure space with respect to (Xi, Si, μi) for i ℃ N. Let X =× Xi, S = ×Si,μ = ×μi. We prove that × L(*Si) CL(*S) and in embedding meaning.展开更多
General expressions of first passage times for denumerable Markov processes are discussed and computation problems for busy periods and waiting times for queues corresponding to Markov processes are studied. In partic...General expressions of first passage times for denumerable Markov processes are discussed and computation problems for busy periods and waiting times for queues corresponding to Markov processes are studied. In particular, the simplified algorithms for busy periods and waiting times for queues corresponding to G//M/1 type and M/G/1 type Markov processes are derived and some numerical examples are presented.展开更多
It is proved that if μ and v be finite measures on a measurable space (X, S) and v is absolutely continuous with respect to v, then it is holds that L(* S, * μ) L(* S, *v), while L(*S, *μ) and L(*S, V) are the Loeb...It is proved that if μ and v be finite measures on a measurable space (X, S) and v is absolutely continuous with respect to v, then it is holds that L(* S, * μ) L(* S, *v), while L(*S, *μ) and L(*S, V) are the Loeb algebras with respect to measure spaces (X, S,μ) and (X,S,v).展开更多
Consider a finite absorbing Markov generator, irreducible on the non-absorbing states. PerronFrobenius theory ensures the existence of a corresponding positive eigenvector ψ. The goal of the paper is to give bounds o...Consider a finite absorbing Markov generator, irreducible on the non-absorbing states. PerronFrobenius theory ensures the existence of a corresponding positive eigenvector ψ. The goal of the paper is to give bounds on the amplitude max ψ/ min ψ. Two approaches are proposed: One using a path method and the other one, restricted to the reversible situation, based on spectral estimates. The latter approach is extended to denumerable birth and death processes absorbing at 0 for which infinity is an entrance boundary. The interest of estimating the ratio is the reduction of the quantitative study of convergence to quasi-stationarity to the convergence to equilibrium of related ergodic processes, as seen by Diaconis and Miclo(2014).展开更多
文摘For a general multidimensional denumerable state Markov process with any initial state probability vector, the probability density function and its LS transform of the first passage time to a certain given state set are obtained and the algorithms for them are derived. It is proved that the resulting errors of the algorithms are both uniform in their respective arguments.Some numerical results are presented.
基金The Special Science Foundation (00jk207) of the Educational Committee of Shaanxi Province.
文摘Let {(Xi, Si, μi) : i ℃ N} be a sequence of probability measure spaces and (*Xi, L(*Si), L(*μi)) be the Loeb measure space with respect to (Xi, Si, μi) for i ℃ N. Let X =× Xi, S = ×Si,μ = ×μi. We prove that × L(*Si) CL(*S) and in embedding meaning.
基金the National Natural Science Foundation of China
文摘General expressions of first passage times for denumerable Markov processes are discussed and computation problems for busy periods and waiting times for queues corresponding to Markov processes are studied. In particular, the simplified algorithms for busy periods and waiting times for queues corresponding to G//M/1 type and M/G/1 type Markov processes are derived and some numerical examples are presented.
基金Supported by the Special Science Foundation of the Education Committee of Shaanxi Province(03jk066)
文摘It is proved that if μ and v be finite measures on a measurable space (X, S) and v is absolutely continuous with respect to v, then it is holds that L(* S, * μ) L(* S, *v), while L(*S, *μ) and L(*S, V) are the Loeb algebras with respect to measure spaces (X, S,μ) and (X,S,v).
基金supported by Agence Nationale de la Recherche(Grant Nos.ANR-11-LABX-0040-CIMIANR-11-IDEX-0002-02 and ANR-12-BS01-0019)
文摘Consider a finite absorbing Markov generator, irreducible on the non-absorbing states. PerronFrobenius theory ensures the existence of a corresponding positive eigenvector ψ. The goal of the paper is to give bounds on the amplitude max ψ/ min ψ. Two approaches are proposed: One using a path method and the other one, restricted to the reversible situation, based on spectral estimates. The latter approach is extended to denumerable birth and death processes absorbing at 0 for which infinity is an entrance boundary. The interest of estimating the ratio is the reduction of the quantitative study of convergence to quasi-stationarity to the convergence to equilibrium of related ergodic processes, as seen by Diaconis and Miclo(2014).
