## Nummelin, Esa

Compute Distance To:
 Author ID: nummelin.esa Published as: Nummelin, E.; Nummelin, Esa External Links: MGP
 Documents Indexed: 46 Publications since 1976, including 1 Book 1 Further Contribution Co-Authors: 8 Co-Authors with 18 Joint Publications 126 Co-Co-Authors
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### Co-Authors

 26 single-authored 7 Ney, Peter E. 4 Arjas, Elja 4 Tweedie, Richard Lewis 2 Niemi, Seppo 2 Tuominen, Pekka 1 Bismut, Jean-Michel 1 Bru, Bernard 1 de Acosta, Alejandro D. 1 Doeblin, Wolfgang 1 Eloranta, Kari 1 Föllmer, Hans 1 Iosifescu, Marius 1 Iscoe, Ian 1 Lindvall, Torgny 1 Seneta, Eugene 1 Yor, Marc
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### Serials

 6 Stochastic Processes and their Applications 5 The Annals of Probability 3 Advances in Applied Probability 3 Mathematica Scandinavica 2 Journal of Statistical Physics 2 Advances in Applied Mathematics 2 Probability Theory and Related Fields 1 Arkhimedes 1 International Journal of Theoretical Physics 1 Advances in Mathematics 1 Annales Academiae Scientiarum Fennicae. Series A I. Mathematica 1 Annales Scientifiques de l’Université de Clermont-Ferrand II. Mathématiques 1 International Statistical Review 1 Journal of Applied Probability 1 Mathematics of Operations Research 1 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 1 Journal of Theoretical Probability 1 The Annals of Applied Probability 1 Annales de l’Institut Henri Poincaré. Nouvelle Série. Section B. Calcul des Probabilités et Statistique 1 Commentationes Physico-Mathematicae 1 Journal of the Australian Mathematical Society. Series A 1 Cambridge Tracts in Mathematics
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### Fields

 43 Probability theory and stochastic processes (60-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 Operator theory (47-XX) 2 Operations research, mathematical programming (90-XX) 1 History and biography (01-XX) 1 Measure and integration (28-XX) 1 Potential theory (31-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Functional analysis (46-XX) 1 Statistics (62-XX) 1 Numerical analysis (65-XX) 1 Computer science (68-XX)

### Citations contained in zbMATH Open

34 Publications have been cited 778 times in 575 Documents Cited by Year
General irreducible Markov chains and non-negative operators. Zbl 0551.60066
Nummelin, Esa
1984
A splitting technique for Harris recurrent Markov chains. Zbl 0364.60104
Nummelin, E.
1978
Markov additive processes. I: Eigenvalue properties and limit theorems. Zbl 0625.60027
Ney, P.; Nummelin, E.
1987
Geometric ergodicity of Harris recurrent Markov chains with applications to renewal theory. Zbl 0484.60056
Nummelin, Esa; Tuominen, Pekka
1982
Markov additive processes. II: Large deviations. Zbl 0625.60028
Ney, P.; Nummelin, E.
1987
Large deviations of uniformly recurrent Markov additive processes. Zbl 0602.60034
Iscoe, I.; Ney, P.; Nummelin, E.
1985
Geometric ergodicity and R-positivity for general Markov chains. Zbl 0378.60051
Nummelin, E.; Tweedie, R. L.
1978
The rate of convergence in Orey’s theorem for Harris recurrent Markov chains with applications to renewal theory. Zbl 0532.60060
Nummelin, Esa; Tuominen, Pekka
1983
The kink of cellular automaton Rule 18 performs a random walk. Zbl 0891.68065
Eloranta, Kari; Nummelin, Esa
1992
Uniform limit theorems for non-singular renewal and Markov renewal processes. Zbl 0375.60095
Arjas, Elja; Nummelin, Esa; Tweedie, Richard L.
1978
On non-singular renewal kernels with an application to a semigroup of transition kernels. Zbl 0606.60080
Niemi, S.; Nummelin, E.
1986
Regeneration in tandem queues. Zbl 0452.60094
Nummelin, E.
1981
Uniform and ratio limit theorems for Markov renewal and semi-regenerative processes on a general state space. Zbl 0402.60087
Nummelin, E.
1978
MC’s for MCMC’ists. Zbl 1217.60062
Nummelin, Esa
2002
Limit theorems for $$\alpha$$-recurrent semi-Markov processes. Zbl 0344.60052
Nummelin, Esa
1976
On the Poisson equation in the potential theory of a single kernel. Zbl 0748.31012
Nummelin, E.
1991
A general failure model: optimal replacement with state dependent replacement and failure costs. Zbl 0442.90029
Nummelin, E.
1980
Strong ratio limit theorems for Phi-recurrent Markov chains. Zbl 0411.60069
Nummelin, E.
1979
A conservation property for general GI/G/1 queues with an application to tandem queues. Zbl 0411.60093
Nummelin, E.
1979
Renewal representations for Markov operators. Zbl 0746.60071
Nummelin, Esa
1991
Large deviations for functionals of stationary processes. Zbl 0685.60029
Nummelin, Esa
1990
Semi-Markov processes on a general state space: alpha-theory and quasi- stationarity. Zbl 0464.60085
Arjas, E.; Nummelin, E.; Tweedie, R. L.
1980
Central limit theorems for Markov random walks. Zbl 0485.60020
Niemi, S.; Nummelin, E.
1982
A direct construction of the R-invariant measure for a Markov chain on a general state space. Zbl 0339.60064
Nummelin, Esa; Arjas, Elja
1976
Level I theory of large deviations in the ideal gas. Zbl 0698.60029
Lehtonen, T.; Nummelin, E.
1990
On the existence and convergence of price equilibria for random economies. Zbl 1161.91360
Nummelin, Esa
2000
Large deviations of random vector fields with applications to economics. Zbl 0963.60026
Nummelin, Esa
2000
Large deviation lower bounds for general sequences of random variables. Zbl 0741.60020
de Acosta, Alejandro D.; Ney, P.; Nummelin, E.
1991
Regeneration for chains of infinite order and random maps. Zbl 0818.60075
Ney, Peter; Nummelin, Esa
1993
On distributionally regenerative processes. Zbl 0818.60078
Nummelin, Esa
1994
On the Perron-Frobenius theory for positive operators on an ordered vector space. Zbl 0597.47021
Nummelin, E.
1985
On the concepts of $$\alpha$$-recurrence and $$\alpha$$-transience for Markov renewal processes. Zbl 0349.60090
Nummelin, Esa
1977
The discrete skeleton method and a total variation limit theorem for continuous-time Markov processes. Zbl 0402.60067
Nummelin, E.
1978
Markov additive processes: Large deviations for the continuous time case. Zbl 0649.60031
Ney, Peter; Nummelin, Esa
1987
MC’s for MCMC’ists. Zbl 1217.60062
Nummelin, Esa
2002
On the existence and convergence of price equilibria for random economies. Zbl 1161.91360
Nummelin, Esa
2000
Large deviations of random vector fields with applications to economics. Zbl 0963.60026
Nummelin, Esa
2000
On distributionally regenerative processes. Zbl 0818.60078
Nummelin, Esa
1994
Regeneration for chains of infinite order and random maps. Zbl 0818.60075
Ney, Peter; Nummelin, Esa
1993
The kink of cellular automaton Rule 18 performs a random walk. Zbl 0891.68065
Eloranta, Kari; Nummelin, Esa
1992
On the Poisson equation in the potential theory of a single kernel. Zbl 0748.31012
Nummelin, E.
1991
Renewal representations for Markov operators. Zbl 0746.60071
Nummelin, Esa
1991
Large deviation lower bounds for general sequences of random variables. Zbl 0741.60020
de Acosta, Alejandro D.; Ney, P.; Nummelin, E.
1991
Large deviations for functionals of stationary processes. Zbl 0685.60029
Nummelin, Esa
1990
Level I theory of large deviations in the ideal gas. Zbl 0698.60029
Lehtonen, T.; Nummelin, E.
1990
Markov additive processes. I: Eigenvalue properties and limit theorems. Zbl 0625.60027
Ney, P.; Nummelin, E.
1987
Markov additive processes. II: Large deviations. Zbl 0625.60028
Ney, P.; Nummelin, E.
1987
Markov additive processes: Large deviations for the continuous time case. Zbl 0649.60031
Ney, Peter; Nummelin, Esa
1987
On non-singular renewal kernels with an application to a semigroup of transition kernels. Zbl 0606.60080
Niemi, S.; Nummelin, E.
1986
Large deviations of uniformly recurrent Markov additive processes. Zbl 0602.60034
Iscoe, I.; Ney, P.; Nummelin, E.
1985
On the Perron-Frobenius theory for positive operators on an ordered vector space. Zbl 0597.47021
Nummelin, E.
1985
General irreducible Markov chains and non-negative operators. Zbl 0551.60066
Nummelin, Esa
1984
The rate of convergence in Orey’s theorem for Harris recurrent Markov chains with applications to renewal theory. Zbl 0532.60060
Nummelin, Esa; Tuominen, Pekka
1983
Geometric ergodicity of Harris recurrent Markov chains with applications to renewal theory. Zbl 0484.60056
Nummelin, Esa; Tuominen, Pekka
1982
Central limit theorems for Markov random walks. Zbl 0485.60020
Niemi, S.; Nummelin, E.
1982
Regeneration in tandem queues. Zbl 0452.60094
Nummelin, E.
1981
A general failure model: optimal replacement with state dependent replacement and failure costs. Zbl 0442.90029
Nummelin, E.
1980
Semi-Markov processes on a general state space: alpha-theory and quasi- stationarity. Zbl 0464.60085
Arjas, E.; Nummelin, E.; Tweedie, R. L.
1980
Strong ratio limit theorems for Phi-recurrent Markov chains. Zbl 0411.60069
Nummelin, E.
1979
A conservation property for general GI/G/1 queues with an application to tandem queues. Zbl 0411.60093
Nummelin, E.
1979
A splitting technique for Harris recurrent Markov chains. Zbl 0364.60104
Nummelin, E.
1978
Geometric ergodicity and R-positivity for general Markov chains. Zbl 0378.60051
Nummelin, E.; Tweedie, R. L.
1978
Uniform limit theorems for non-singular renewal and Markov renewal processes. Zbl 0375.60095
Arjas, Elja; Nummelin, Esa; Tweedie, Richard L.
1978
Uniform and ratio limit theorems for Markov renewal and semi-regenerative processes on a general state space. Zbl 0402.60087
Nummelin, E.
1978
The discrete skeleton method and a total variation limit theorem for continuous-time Markov processes. Zbl 0402.60067
Nummelin, E.
1978
On the concepts of $$\alpha$$-recurrence and $$\alpha$$-transience for Markov renewal processes. Zbl 0349.60090
Nummelin, Esa
1977
Limit theorems for $$\alpha$$-recurrent semi-Markov processes. Zbl 0344.60052
Nummelin, Esa
1976
A direct construction of the R-invariant measure for a Markov chain on a general state space. Zbl 0339.60064
Nummelin, Esa; Arjas, Elja
1976
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### Cited by 630 Authors

 17 Nummelin, Esa 14 Glynn, Peter W. 12 Roberts, Gareth O. 11 Meyn, Sean P. 11 Rosenthal, Jeffrey S. 10 Fuh, Cheng-Der 9 Bertail, Patrice 7 Clémençon, Stéphan 7 Collamore, Jeffrey F. 7 Golomozyĭ, V. V. 7 Hobert, James P. 7 Ney, Peter E. 7 Tweedie, Richard Lewis 6 Alsmeyer, Gerold 6 Guillin, Arnaud 6 Löcherbach, Eva 6 Miyazawa, Masakiyo 6 Tjøstheim, Dag B. 5 Athreya, Krishna Balasundaram 5 de Acosta, Alejandro D. 5 Fort, Gersende 5 Kartashov, Mykola Valentynovych 5 Lee, Oesook 5 Macci, Claudio 5 Mukhamedov, Farruh Maksutovich 5 Nagaev, Sergey Victorovich 5 Wu, Liming 5 Yu, Huizhen 4 Chan, Hock Peng 4 Chen, Xia 4 Foss, Sergey G. 4 Gordienko, Evgueni I. 4 Jones, Galin L. 4 Kamatani, Kengo 4 Karlsen, Hans Arnfinn 4 Li, Degui 4 Morozov, Evsei 4 Moulines, Eric 4 Nguyen, Dang Hai 4 Nyrhinen, Harri 4 Rio, Emmanuel 4 Robert, Philippe 4 Shur, Mikhail Grigoryevtsh 4 Thorisson, Hermann 4 Veretennikov, Alexander Yu. 3 Adamczak, Radosław 3 Asmussen, Søren 3 Bednorz, Witold Marek 3 Borovkov, Aleksandr Alekseevich 3 Ciołek, Gabriela 3 Dedecker, Jérôme 3 Douc, Randal 3 Dupuis, Paul G. 3 Geyer, Charles J. 3 Gravner, Janko 3 Harel, Michel 3 Hu, Inchi 3 Jensen, Uwe 3 Lai, Tze Leung 3 Latuszynski, Krzysztof 3 McDonald, David R. 3 Mentemeier, Sebastian 3 Mogul’skii, Anatolii Alfredovich 3 Montes-de-Oca, Raúl 3 Myklebust, Terje 3 Puri, Madan Lal 3 Roitershtein, Alexander 3 Sgibnev, Mikhaĭl Sergeevich 3 Sigman, Karl 3 Sokal, Alan D. 3 Thomas, Lawrence E. 3 Tressou, Jessica 3 Vihola, Matti 3 Zhao, Yiqiang Q. 2 Aaronson, Jon 2 Agapie, Alexandru 2 Agapie, Mircea 2 Aldous, David John 2 Andrieu, Christophe 2 Arjas, Elja 2 Bandi, Federico M. 2 Baxendale, Peter H. 2 Ben-Ari, Iddo 2 Bladt, Mogens 2 Bolthausen, Erwin 2 Bou-Rabee, Nawaf M. 2 Bradley, Richard C. jun. 2 Bramson, Maury D. 2 Butkovsky, Oleg A. 2 Chan, Nigel H. N. 2 Crutchfield, James P. 2 De Gregorio, Alessandro 2 Dembo, Amir 2 Doukhan, Paul 2 Duffield, Nick G. 2 El-Gamal, Mahmoud A. 2 Erhardsson, Torkel 2 Foley, Robert D. 2 Gao, Jiti 2 Guo, Lei ...and 530 more Authors
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### Cited in 164 Serials

 78 Stochastic Processes and their Applications 45 The Annals of Applied Probability 28 Statistics & Probability Letters 18 The Annals of Probability 18 Probability Theory and Related Fields 18 Queueing Systems 16 Journal of Theoretical Probability 14 Journal of Statistical Physics 12 Advances in Applied Probability 12 Journal of Applied Probability 11 The Annals of Statistics 9 Bernoulli 7 Journal of Econometrics 7 Theory of Probability and Mathematical Statistics 6 Journal of Time Series Analysis 6 Acta Applicandae Mathematicae 6 Communications in Statistics. Theory and Methods 6 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 6 Stochastic Models 5 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 5 Journal of Mathematical Sciences (New York) 5 Econometric Theory 4 Journal of Mathematical Analysis and Applications 4 Mathematical Notes 4 Theory of Probability and its Applications 4 Journal of Multivariate Analysis 4 Journal of Statistical Planning and Inference 4 SIAM Journal on Control and Optimization 4 Advances in Applied Mathematics 4 Operations Research Letters 4 Communications in Statistics. Simulation and Computation 4 Journal of Nonparametric Statistics 4 Methodology and Computing in Applied Probability 4 Electronic Journal of Statistics 3 The Canadian Journal of Statistics 3 Lithuanian Mathematical Journal 3 Journal of Differential Equations 3 Journal of Soviet Mathematics 3 Siberian Mathematical Journal 3 Transactions of the American Mathematical Society 3 OR Spektrum 3 Annals of Operations Research 3 Automation and Remote Control 3 Computational Statistics and Data Analysis 3 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 3 Positivity 3 Probability in the Engineering and Informational Sciences 2 Communications on Pure and Applied Mathematics 2 Journal of Mathematical Biology 2 Metrika 2 Annals of the Institute of Statistical Mathematics 2 Fuzzy Sets and Systems 2 Journal of Functional Analysis 2 Kybernetika 2 Mathematica Slovaca 2 Proceedings of the American Mathematical Society 2 Scandinavian Actuarial Journal 2 Theoretical Computer Science 2 Ergodic Theory and Dynamical Systems 2 Stochastic Analysis and Applications 2 Physica D 2 Acta Mathematicae Applicatae Sinica. English Series 2 Optimization 2 European Journal of Operational Research 2 Stochastics and Stochastics Reports 2 Electronic Communications in Probability 2 Doklady Mathematics 2 Mathematical Methods of Operations Research 2 Discrete and Continuous Dynamical Systems. Series B 2 Multiscale Modeling & Simulation 2 Journal of Probability and Statistics 2 European Actuarial Journal 2 Statistics and Computing 1 Bulletin of the Australian Mathematical Society 1 Communications in Mathematical Physics 1 International Journal of Systems Science 1 Israel Journal of Mathematics 1 Journal d’Analyse Mathématique 1 Journal of Computational Physics 1 Linear and Multilinear Algebra 1 Physica A 1 Problems of Information Transmission 1 Reviews of Modern Physics 1 Russian Mathematical Surveys 1 Scandinavian Journal of Statistics 1 Bulletin of Mathematical Biology 1 Advances in Mathematics 1 Annales Scientifiques de l’Université de Clermont-Ferrand II. Mathématiques 1 Automatica 1 Glasgow Mathematical Journal 1 Inventiones Mathematicae 1 Journal of the American Statistical Association 1 Journal of Computational and Applied Mathematics 1 Journal of Mathematical Economics 1 Journal of Optimization Theory and Applications 1 Mathematics and Computers in Simulation 1 Mathematics of Operations Research 1 Mathematische Zeitschrift 1 Memoirs of the American Mathematical Society 1 Operations Research ...and 64 more Serials
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### Cited in 35 Fields

 475 Probability theory and stochastic processes (60-XX) 113 Statistics (62-XX) 73 Numerical analysis (65-XX) 55 Operations research, mathematical programming (90-XX) 37 Dynamical systems and ergodic theory (37-XX) 28 Statistical mechanics, structure of matter (82-XX) 27 Systems theory; control (93-XX) 26 Computer science (68-XX) 23 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 21 Biology and other natural sciences (92-XX) 18 Operator theory (47-XX) 10 Measure and integration (28-XX) 7 Ordinary differential equations (34-XX) 7 Partial differential equations (35-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 5 Integral equations (45-XX) 3 Combinatorics (05-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Information and communication theory, circuits (94-XX) 2 History and biography (01-XX) 2 Number theory (11-XX) 2 Topological groups, Lie groups (22-XX) 2 Difference and functional equations (39-XX) 2 Convex and discrete geometry (52-XX) 1 Mathematical logic and foundations (03-XX) 1 Group theory and generalizations (20-XX) 1 Real functions (26-XX) 1 Approximations and expansions (41-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral transforms, operational calculus (44-XX) 1 Functional analysis (46-XX) 1 General topology (54-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Quantum theory (81-XX)