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## Marcus, Michael B.

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 Author ID: marcus.michael-b Published as: Marcus, M.; Marcus, M. B.; Marcus, Michael; Marcus, Michael B.; Marcus, Michel B. Homepage: http://home.earthlink.net/~mbmarcus/ External Links: MGP
 Documents Indexed: 122 Publications since 1963, including 11 Books
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#### Co-Authors

 33 single-authored 38 Rosen, Jay S. 7 Pisier, Gilles 6 Giné-Masdéu, Evarist 6 Jain, Naresh C. 6 Zinn, Joel 5 Rosiński, Jan 3 Boas, Ralph Philip jun. 3 Kuelbs, James D. 3 Talagrand, Michel 3 Woyczynski, Wojbor A. 2 Hoffmann-Jørgensen, Jørgen 2 Kogan, Hana 2 Le Jan, Yves 2 Shepp, Lawrence Alan 1 Adler, Robert Joseph 1 Beck, Anatole 1 Bussgang, J. J. 1 Chen, Xia 1 de Araujo, Aloisio Pessoa 1 Dobric, Vladimir 1 Dudley, Richard Mansfield 1 Eberlein, Ernst W. 1 Eisenbaum, Nathalie 1 Fernique, Xavier 1 Hahn, Marjorie Green 1 Heinkel, Bernard 1 Iscoe, Ian 1 Kaspi, Haya 1 Kwapień, Stanisław 1 Ledoux, Michel 1 Li, Wenbo V. 1 McDonald, David R. 1 Meyer, Paul-André 1 Peskir, Goran 1 Philipp, Walter 1 Pinsky, Mark Allan 1 Sacks, Jerome 1 Shen, Kevin H. W. 1 Shi, Zhan 1 Weber, Michel Jean Georges 1 Wellner, Jon August
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#### Serials

 22 The Annals of Probability 7 Stochastic Processes and their Applications 6 Journal of Theoretical Probability 5 Transactions of the American Mathematical Society 4 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 4 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 4 Electronic Communications in Probability 3 Journal of Functional Analysis 3 Memoirs of the American Mathematical Society 3 Electronic Journal of Probability 3 Progress in Probability 2 Journal of Mathematical Analysis and Applications 2 Annales de l’Institut Fourier 2 Lecture Notes in Mathematics 2 Annals of Mathematical Statistics 1 American Mathematical Monthly 1 Arkiv för Matematik 1 Mathematics Magazine 1 Acta Mathematica 1 Colloquium Mathematicum 1 Journal of Approximation Theory 1 Journal of Optimization Theory and Applications 1 Osaka Journal of Mathematics 1 Pacific Journal of Mathematics 1 Probability and Mathematical Statistics 1 SIAM Journal on Mathematical Analysis 1 Bulletin of the American Mathematical Society. New Series 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A 1 Annals of Mathematics Studies 1 Cambridge Studies in Advanced Mathematics 1 Lecture Notes Series. Aarhus University 1 Communications on Stochastic Analysis
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#### Fields

 112 Probability theory and stochastic processes (60-XX) 7 Functional analysis (46-XX) 6 General and overarching topics; collections (00-XX) 3 Real functions (26-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Abstract harmonic analysis (43-XX) 3 Statistics (62-XX) 1 History and biography (01-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Functions of a complex variable (30-XX) 1 Sequences, series, summability (40-XX) 1 Approximations and expansions (41-XX)

#### Citations contained in zbMATH

94 Publications have been cited 881 times in 638 Documents Cited by Year
Markov processes, Gaussian processes, and local times. Zbl 1129.60002
Marcus, Michael B.; Rosen, Jay
2006
Random Fourier series with applications to harmonic analysis. Zbl 0474.43004
Marcus, Michael B.; Pisier, Gilles
1981
Characterizations of almost surely continuous p-stable random Fourier series and strongly stationary processes. Zbl 0547.60047
Marcus, M. B.; Pisier, G.
1984
Central limit theorems for C(S)-valued random variables. Zbl 0305.60004
Jain, Naresh C.; Marcus, Michael B.
1975
Sample behavior of Gaussian processes. Zbl 0379.60040
Marcus, M. B.; Shepp, L. A.
1972
Sample path properties of the local times of strongly symmetric Markov processes via Gaussian processes. Zbl 0762.60068
Marcus, Michael B.; Rosen, Jay
1992
A Ray-Knight theorem for symmetric Markov processes. Zbl 1044.60064
Eisenbaum, Nathalie; Kaspi, Haya; Marcus, Michael B.; Rosen, Jay; Shi, Zhan
2000
Weak convergence of the empirical characteristic function. Zbl 0465.60008
Marcus, Michael B.
1981
$$p$$-variation of the local times of symmetric stable processes and of Gaussian processes with stationary increments. Zbl 0762.60069
Marcus, Michael B.; Rosen, Jay
1992
Continuity of $$\ell ^ 2$$-valued Ornstein-Uhlenbeck processes. Zbl 0699.60052
Iscoe, I.; Marcus, M. B.; McDonald, D.; Talagrand, M.; Zinn, J.
1990
$$\xi$$-radial processes and random Fourier series. Zbl 0636.60039
Marcus, Michael B.
1987
Stable measures and central limit theorems in spaces of stable type. Zbl 0449.60003
Marcus, Michael B.; Woyczynski, Wojbor A.
1979
Integrability of infinite sums of independent vector-valued random variables. Zbl 0318.60036
Jain, Naresh C.; Marcus, Michael B.
1975
Continuity of Gaussian processes. Zbl 0209.49201
Marcus, M. B.; Shepp, L. A.
1970
Hölder conditions for Gaussian processes with stationary increments. Zbl 0186.50602
Marcus, M. B.
1968
Continuity and boundedness of infinitely divisible processes: A Poisson point process approach. Zbl 1071.60025
Marcus, Michael B.; Rosiński, Jan
2005
Level crossings of a stochastic process with absolutely continuous sample paths. Zbl 0364.60063
Marcus, Michael B.
1977
Sufficient conditions for the continuity of stationary Gaussian processes and applications to random series of functions. Zbl 0283.60041
Jain, Naresh C.; Marcus, M. B.
1974
Upper bounds for the asymptotic maxima of continuous Gaussian processes. Zbl 0241.60032
Marcus, M. B.
1972
A bound for the distribution of the maximum of continuous Gaussian processes. Zbl 0234.60054
Marcus, Michael
1970
Laws of the iterated logarithm for the local times of symmetric Lévy processes and recurrent random walks. Zbl 0815.60073
Marcus, Michael B.; Rosen, Jay
1994
Gaussian chaos and sample path properties of additive functionals of symmetric Markov processes. Zbl 0862.60065
Marcus, Michael B.; Rosen, Jay
1996
The bounded law of the iterated logarithm for the weighted empirical distribution process in the non-i.i.d. case. Zbl 0538.60009
Marcus, Michael B.; Zinn, Joel
1984
Some results on the continuity of stable processes and the domain of attraction of continuous stable processes. Zbl 0536.60048
Marcus, M. B.; Pisier, G.
1984
Two results on continuity and boundedness of stochastic convolutions. Zbl 1106.60040
Kwapień, Stanisław; Marcus, Michael B.; Rosiński, Jan
2006
Renormalized self-intersection local times and Wick power chaos processes. Zbl 1230.60005
Marcus, Michael B.; Rosen, Jay
1999
The central limit theorem for stochastic integrals with respect to Levy processes. Zbl 0504.60011
Gine, Evarist; Marcus, Michel B.
1983
The most visited sites of certain Lévy processes. Zbl 0991.60035
Marcus, Michael B.
2001
$$L^1$$-norm of infinitely divisible random vectors and certain stochastic integrals. Zbl 0976.60027
Marcus, Michael B.; Rosiński, Jan
2001
Laws of the iterated logarithm for intersections of random walks on $$Z^ 4$$. Zbl 0870.60065
Marcus, Michael B.; Rosen, Jay
1997
Logarithmic averages for the local times of recurrent random walks and Lévy processes. Zbl 0853.60059
Marcus, Michael B.; Rosen, Jay
1995
Almost sure invariance principles for sums of B-valued random variables with applications to random Fourier series and the empirical characteristic process. Zbl 0485.60030
Marcus, Michael B.; Philipp, Walter
1982
Gaussian processes with stationary increments possessing discontinuous sample paths. Zbl 0245.60035
Marcus, Michael B.
1968
Permanental fields, loop soups and continuous additive functionals. Zbl 1316.60075
Le Jan, Yves; Marcus, Michael B.; Rosen, Jay
2015
Some bounds for the expected number of level crossings of symmetric harmonizable p-stable processes. Zbl 0693.60027
Marcus, Michael B.
1989
Continuity and the central limit theorem for random trigonometric series. Zbl 0382.60041
Marcus, Michael B.
1978
Robust designs for regression problems. Zbl 0422.62067
Marcus, Michael B.; Sacks, Jerome
1977
An almost sure limit theorem for Wick powers of Gaussian differences quotients. Zbl 1243.60036
Marcus, Michael B.; Rosen, Jay
2009
Laws of the iterated logarithm for the local times of recurrent random walks on $$Z^ 2$$ and of Lévy processes and random walks in the domain of attraction of Cauchy random variables. Zbl 0805.60069
Marcus, Michael B.; Rosen, Jay
1994
A sufficient condition for the continuity of permanental processes with applications to local times of Markov processes. Zbl 1329.60273
Marcus, Michael B.; Rosen, Jay
2013
A CLT for the $$L^{2}$$ modulus of continuity of Brownian local time. Zbl 1190.60071
Chen, Xia; Li, Wenbo V.; Marcus, Michael B.; Rosen, Jay
2010
CLT for $$L^p$$ moduli of continuity of Gaussian processes. Zbl 1147.60015
Marcus, Michael B.; Rosen, Jay
2008
$$L^p$$ moduli of continuity of Gaussian processes and local times of symmetric Lévy processes. Zbl 1260.60156
Marcus, Michael B.; Rosen, Jay
2008
Gaussian processes and local times of symmetric Lévy processes. Zbl 0988.60026
Marcus, Michael B.; Rosen, Jay
2001
Extreme values for sequences of stable random variables. Zbl 0569.60009
Marcus, Michael B.
1984
Necessary and sufficient conditions for the uniform convergence of random trigonometric series. Zbl 0409.60036
Marcus, M. B.; Pisier, G.
1978
Capacity of level sets of certain stochastic processes. Zbl 0368.60038
Marcus, Michael B.
1976
Uniform convergence of random Fourier series. Zbl 0317.42008
Marcus, Michael B.
1975
Continuity of Gaussian processes and random Fourier series. Zbl 0277.60022
Marcus, M. B.
1973
Intersection local times, loop soups and permanental Wick powers. Zbl 1368.60080
Le Jan, Yves; Marcus, Michael B.; Rosen, Jay
2017
Permanental processes. Zbl 1331.60002
Kogan, Hana; Marcus, Michael B.; Rosen, Jay
2011
Probability estimates for lower levels of certain Gaussian processes with stationary increments. Zbl 0973.60040
Marcus, Michael B.
2000
$$\Phi$$-variation of the local times of symmetric Lévy processes and stationary Gaussian processes. Zbl 0793.60043
Marcus, Michael B.; Rosen, Jay
1992
Central limit theorems for the local times of certain Markov processes and the squares of Gaussian processes. Zbl 0722.60078
Adler, Robert J.; Marcus, Michael B.; Zinn, Joel
1990
The distribution of large values of the supremum of a Gaussian process. Zbl 0659.60061
Dobric, Vladimir; Marcus, Michael B.; Weber, Michel
1988
Stochastic processes with sample paths in exponential Orlicz spaces. Zbl 0576.60031
Marcus, Michael B.; Pisier, Gilles
1985
The $$\varepsilon$$-entropy of some compact subsets of l$$^p$$. Zbl 0277.60023
Marcus, M. B.
1974
A comparison of continuity conditions for Gaussian processes. Zbl 0265.60039
Marcus, M. B.
1973
Inequalities involving a function and its inverse. Zbl 0235.26009
Boas, R. P. jun.; Marcus, M. B.
1973
Gaussian lacunary series and the modulus of continuity for Gaussian processes. Zbl 0222.60026
Marcus, M. B.
1972
Hölder conditions for continuous Gaussian processes. Zbl 0255.60027
Marcus, Michael B.
1970
On the domain of attraction of $$e^{-e^{-x}}$$. Zbl 0169.50201
Marcus, Michael; Pinsky, M.
1969
Conditions for permanental processes to be unbounded. Zbl 1386.60331
Marcus, Michael B.; Rosen, Jay
2017
Sufficient conditions for boundedness of moving average processes. Zbl 1043.60030
Marcus, Michael B.; Rosiński, Jan
2003
Additive functionals of several Lévy processes and intersection local times. Zbl 0963.60072
Marcus, Michael B.; Rosen, Jay
1999
A sufficient condition for the continuity of high order Gaussian chaos processes. Zbl 0905.60026
Marcus, Michael B.
1998
Moment generating functions for local times of symmetric Markov processes and random walks. Zbl 0788.60092
Marcus, Michael B.; Rosen, Jay
1992
Moduli of continuity of local times of strongly symmetric Markov processes via Gaussian processes. Zbl 0761.60035
Marcus, Michael B.; Rosen, Jay
1992
A version of Chevet’s theorem for stable processes. Zbl 0659.60007
Giné, Evarist; Marcus, Michael B.; Zinn, Joel
1985
Probability in Banach spaces V. Proceedings of the Fifth International Conference held in Medford, Massachusetts, USA, July 16-27, 1984. Zbl 0563.00014
Beck, A. (ed.); Dudley, R. (ed.); Hahn, M. (ed.); Kuelbs, J. (ed.); Marcus, M. (ed.)
1985
Some results on the domain of attraction of stable measures on C(K). Zbl 0535.60010
Giné, Evarist; Marcus, Michael B.
1982
Stable processes with continuous sample paths. Zbl 0407.60040
de Araujo, Aloisio Pessoa; Marcus, M. B.
1979
Asymptotic maxima of continuous Gaussian processes. Zbl 0304.60024
Marcus, M. B.
1974
Inverse functions and integration by parts. Zbl 0285.26008
Boas, R. P. jun.; Marcus, M. B.
1974
Generalizations of Young’s inequality. Zbl 0275.26021
Boas, R. P. jun.; Marcus, M. B.
1974
A new proof of a sufficient condition for discontinuity of Gaussian processes. Zbl 0257.60015
Jain, N. C.; Marcus, M. B.
1973
Permanental processes with kernels that are not equivalent to a symmetric matrix. Zbl 1448.60194
Marcus, Michael B.; Rosen, Jay
2019
Sample path properties of permanental processes. Zbl 1410.60068
Marcus, Michael B.; Rosen, Jay
2018
Permanental random variables, $$M$$-matrices and $$\alpha$$-permanents. Zbl 1382.60034
Marcus, Michael B.; Rosen, Jay
2016
Multivariate gamma distributions. Zbl 1321.60023
Marcus, Michael B.
2014
Permanental vectors. Zbl 1255.60027
Kogan, Hana; Marcus, Michael B.
2012
Existence of a critical point for the infinite divisibility of squares of Gaussian vectors in $$\mathbb R^{2}$$ with non-zero mean. Zbl 1191.60020
Rosen, Jay S.; Marcus, Michael B.
2009
High dimensional probability III. Third international conference on high dimensional probability, Sandjberg, Denmark, June 24–28, 2002. Selected papers. Zbl 1029.00032
Hoffmann-Jørgensen, Jørgen (ed.); Marcus, Michael B. (ed.); Wellner, Jon A. (ed.)
2003
Multiple Wick product chaos processes. Zbl 1105.60304
Marcus, Michael B.; Rosen, Jay
1999
Bounds for the expected number of level crossings of certain harmonizable infinitely divisible processes. Zbl 0932.60035
Marcus, Michael B.; Shen, Kevin
1998
Continuity conditions for a class of Gaussian chaos processes related to continuous additive functionals of Lévy processes. Zbl 0899.60034
Marcus, Michael B.; Talagrand, Michel
1998
Probability in Banach spaces, 9: Proceedings from the 9th international conference on probability in Banach spaces, held at Sandjberg, Denmark, August 16-21, 1993. Zbl 0799.00028
Hoffmann-Jørgensen, Jørgen (ed.); Kuelbs, James (ed.); Marcus, Michael B. (ed.)
1994
On random multipliers in the central limit theorem with p-stable limit, $$0<p<2$$. Zbl 0699.60007
Giné, Evarist; Marcus, Michael B.; Zinn, Joel
1990
A version of Chevet’s theorem for stable processes. Zbl 0654.60009
Giné, Evarist; Marcus, Michael B.; Zinn, Joel
1985
On the central limit theorem in C(K). Zbl 0516.60011
Gine, Evarist; Marcus, Michael B.
1981
Random Fourier series on locally compact Abelian groups. Zbl 0413.60004
Marcus, M. B.; Pisier, G.
1979
Domaine d’attraction normal dans les espaces de type stable p. Zbl 0368.60025
Marcus, Michael B.; Woyczynski, Wojbor A.
1977
Sufficient conditions for the continuity of stationary Gaussian processes and applications to random series of functions. Zbl 0336.60041
Jain, Naresh C.; Marcus, M. B.
1975
Sufficient conditions for the continuity of stationary Gaussian processes and applications to random series of functions. Zbl 0275.60053
Jain, Naresh C.; Marcus, M. B.
1974
Permanental processes with kernels that are not equivalent to a symmetric matrix. Zbl 1448.60194
Marcus, Michael B.; Rosen, Jay
2019
Sample path properties of permanental processes. Zbl 1410.60068
Marcus, Michael B.; Rosen, Jay
2018
Intersection local times, loop soups and permanental Wick powers. Zbl 1368.60080
Le Jan, Yves; Marcus, Michael B.; Rosen, Jay
2017
Conditions for permanental processes to be unbounded. Zbl 1386.60331
Marcus, Michael B.; Rosen, Jay
2017
Permanental random variables, $$M$$-matrices and $$\alpha$$-permanents. Zbl 1382.60034
Marcus, Michael B.; Rosen, Jay
2016
Permanental fields, loop soups and continuous additive functionals. Zbl 1316.60075
Le Jan, Yves; Marcus, Michael B.; Rosen, Jay
2015
Multivariate gamma distributions. Zbl 1321.60023
Marcus, Michael B.
2014
A sufficient condition for the continuity of permanental processes with applications to local times of Markov processes. Zbl 1329.60273
Marcus, Michael B.; Rosen, Jay
2013
Permanental vectors. Zbl 1255.60027
Kogan, Hana; Marcus, Michael B.
2012
Permanental processes. Zbl 1331.60002
Kogan, Hana; Marcus, Michael B.; Rosen, Jay
2011
A CLT for the $$L^{2}$$ modulus of continuity of Brownian local time. Zbl 1190.60071
Chen, Xia; Li, Wenbo V.; Marcus, Michael B.; Rosen, Jay
2010
An almost sure limit theorem for Wick powers of Gaussian differences quotients. Zbl 1243.60036
Marcus, Michael B.; Rosen, Jay
2009
Existence of a critical point for the infinite divisibility of squares of Gaussian vectors in $$\mathbb R^{2}$$ with non-zero mean. Zbl 1191.60020
Rosen, Jay S.; Marcus, Michael B.
2009
CLT for $$L^p$$ moduli of continuity of Gaussian processes. Zbl 1147.60015
Marcus, Michael B.; Rosen, Jay
2008
$$L^p$$ moduli of continuity of Gaussian processes and local times of symmetric Lévy processes. Zbl 1260.60156
Marcus, Michael B.; Rosen, Jay
2008
Markov processes, Gaussian processes, and local times. Zbl 1129.60002
Marcus, Michael B.; Rosen, Jay
2006
Two results on continuity and boundedness of stochastic convolutions. Zbl 1106.60040
Kwapień, Stanisław; Marcus, Michael B.; Rosiński, Jan
2006
Continuity and boundedness of infinitely divisible processes: A Poisson point process approach. Zbl 1071.60025
Marcus, Michael B.; Rosiński, Jan
2005
Sufficient conditions for boundedness of moving average processes. Zbl 1043.60030
Marcus, Michael B.; Rosiński, Jan
2003
High dimensional probability III. Third international conference on high dimensional probability, Sandjberg, Denmark, June 24–28, 2002. Selected papers. Zbl 1029.00032
Hoffmann-Jørgensen, Jørgen (ed.); Marcus, Michael B. (ed.); Wellner, Jon A. (ed.)
2003
The most visited sites of certain Lévy processes. Zbl 0991.60035
Marcus, Michael B.
2001
$$L^1$$-norm of infinitely divisible random vectors and certain stochastic integrals. Zbl 0976.60027
Marcus, Michael B.; Rosiński, Jan
2001
Gaussian processes and local times of symmetric Lévy processes. Zbl 0988.60026
Marcus, Michael B.; Rosen, Jay
2001
A Ray-Knight theorem for symmetric Markov processes. Zbl 1044.60064
Eisenbaum, Nathalie; Kaspi, Haya; Marcus, Michael B.; Rosen, Jay; Shi, Zhan
2000
Probability estimates for lower levels of certain Gaussian processes with stationary increments. Zbl 0973.60040
Marcus, Michael B.
2000
Renormalized self-intersection local times and Wick power chaos processes. Zbl 1230.60005
Marcus, Michael B.; Rosen, Jay
1999
Additive functionals of several Lévy processes and intersection local times. Zbl 0963.60072
Marcus, Michael B.; Rosen, Jay
1999
Multiple Wick product chaos processes. Zbl 1105.60304
Marcus, Michael B.; Rosen, Jay
1999
A sufficient condition for the continuity of high order Gaussian chaos processes. Zbl 0905.60026
Marcus, Michael B.
1998
Bounds for the expected number of level crossings of certain harmonizable infinitely divisible processes. Zbl 0932.60035
Marcus, Michael B.; Shen, Kevin
1998
Continuity conditions for a class of Gaussian chaos processes related to continuous additive functionals of Lévy processes. Zbl 0899.60034
Marcus, Michael B.; Talagrand, Michel
1998
Laws of the iterated logarithm for intersections of random walks on $$Z^ 4$$. Zbl 0870.60065
Marcus, Michael B.; Rosen, Jay
1997
Gaussian chaos and sample path properties of additive functionals of symmetric Markov processes. Zbl 0862.60065
Marcus, Michael B.; Rosen, Jay
1996
Logarithmic averages for the local times of recurrent random walks and Lévy processes. Zbl 0853.60059
Marcus, Michael B.; Rosen, Jay
1995
Laws of the iterated logarithm for the local times of symmetric Lévy processes and recurrent random walks. Zbl 0815.60073
Marcus, Michael B.; Rosen, Jay
1994
Laws of the iterated logarithm for the local times of recurrent random walks on $$Z^ 2$$ and of Lévy processes and random walks in the domain of attraction of Cauchy random variables. Zbl 0805.60069
Marcus, Michael B.; Rosen, Jay
1994
Probability in Banach spaces, 9: Proceedings from the 9th international conference on probability in Banach spaces, held at Sandjberg, Denmark, August 16-21, 1993. Zbl 0799.00028
Hoffmann-Jørgensen, Jørgen (ed.); Kuelbs, James (ed.); Marcus, Michael B. (ed.)
1994
Sample path properties of the local times of strongly symmetric Markov processes via Gaussian processes. Zbl 0762.60068
Marcus, Michael B.; Rosen, Jay
1992
$$p$$-variation of the local times of symmetric stable processes and of Gaussian processes with stationary increments. Zbl 0762.60069
Marcus, Michael B.; Rosen, Jay
1992
$$\Phi$$-variation of the local times of symmetric Lévy processes and stationary Gaussian processes. Zbl 0793.60043
Marcus, Michael B.; Rosen, Jay
1992
Moment generating functions for local times of symmetric Markov processes and random walks. Zbl 0788.60092
Marcus, Michael B.; Rosen, Jay
1992
Moduli of continuity of local times of strongly symmetric Markov processes via Gaussian processes. Zbl 0761.60035
Marcus, Michael B.; Rosen, Jay
1992
Continuity of $$\ell ^ 2$$-valued Ornstein-Uhlenbeck processes. Zbl 0699.60052
Iscoe, I.; Marcus, M. B.; McDonald, D.; Talagrand, M.; Zinn, J.
1990
Central limit theorems for the local times of certain Markov processes and the squares of Gaussian processes. Zbl 0722.60078
Adler, Robert J.; Marcus, Michael B.; Zinn, Joel
1990
On random multipliers in the central limit theorem with p-stable limit, $$0<p<2$$. Zbl 0699.60007
Giné, Evarist; Marcus, Michael B.; Zinn, Joel
1990
Some bounds for the expected number of level crossings of symmetric harmonizable p-stable processes. Zbl 0693.60027
Marcus, Michael B.
1989
The distribution of large values of the supremum of a Gaussian process. Zbl 0659.60061
Dobric, Vladimir; Marcus, Michael B.; Weber, Michel
1988
$$\xi$$-radial processes and random Fourier series. Zbl 0636.60039
Marcus, Michael B.
1987
Stochastic processes with sample paths in exponential Orlicz spaces. Zbl 0576.60031
Marcus, Michael B.; Pisier, Gilles
1985
A version of Chevet’s theorem for stable processes. Zbl 0659.60007
Giné, Evarist; Marcus, Michael B.; Zinn, Joel
1985
Probability in Banach spaces V. Proceedings of the Fifth International Conference held in Medford, Massachusetts, USA, July 16-27, 1984. Zbl 0563.00014
Beck, A. (ed.); Dudley, R. (ed.); Hahn, M. (ed.); Kuelbs, J. (ed.); Marcus, M. (ed.)
1985
A version of Chevet’s theorem for stable processes. Zbl 0654.60009
Giné, Evarist; Marcus, Michael B.; Zinn, Joel
1985
Characterizations of almost surely continuous p-stable random Fourier series and strongly stationary processes. Zbl 0547.60047
Marcus, M. B.; Pisier, G.
1984
The bounded law of the iterated logarithm for the weighted empirical distribution process in the non-i.i.d. case. Zbl 0538.60009
Marcus, Michael B.; Zinn, Joel
1984
Some results on the continuity of stable processes and the domain of attraction of continuous stable processes. Zbl 0536.60048
Marcus, M. B.; Pisier, G.
1984
Extreme values for sequences of stable random variables. Zbl 0569.60009
Marcus, Michael B.
1984
The central limit theorem for stochastic integrals with respect to Levy processes. Zbl 0504.60011
Gine, Evarist; Marcus, Michel B.
1983
Almost sure invariance principles for sums of B-valued random variables with applications to random Fourier series and the empirical characteristic process. Zbl 0485.60030
Marcus, Michael B.; Philipp, Walter
1982
Some results on the domain of attraction of stable measures on C(K). Zbl 0535.60010
Giné, Evarist; Marcus, Michael B.
1982
Random Fourier series with applications to harmonic analysis. Zbl 0474.43004
Marcus, Michael B.; Pisier, Gilles
1981
Weak convergence of the empirical characteristic function. Zbl 0465.60008
Marcus, Michael B.
1981
On the central limit theorem in C(K). Zbl 0516.60011
Gine, Evarist; Marcus, Michael B.
1981
Stable measures and central limit theorems in spaces of stable type. Zbl 0449.60003
Marcus, Michael B.; Woyczynski, Wojbor A.
1979
Stable processes with continuous sample paths. Zbl 0407.60040
de Araujo, Aloisio Pessoa; Marcus, M. B.
1979
Random Fourier series on locally compact Abelian groups. Zbl 0413.60004
Marcus, M. B.; Pisier, G.
1979
Continuity and the central limit theorem for random trigonometric series. Zbl 0382.60041
Marcus, Michael B.
1978
Necessary and sufficient conditions for the uniform convergence of random trigonometric series. Zbl 0409.60036
Marcus, M. B.; Pisier, G.
1978
Level crossings of a stochastic process with absolutely continuous sample paths. Zbl 0364.60063
Marcus, Michael B.
1977
Robust designs for regression problems. Zbl 0422.62067
Marcus, Michael B.; Sacks, Jerome
1977
Domaine d’attraction normal dans les espaces de type stable p. Zbl 0368.60025
Marcus, Michael B.; Woyczynski, Wojbor A.
1977
Capacity of level sets of certain stochastic processes. Zbl 0368.60038
Marcus, Michael B.
1976
Central limit theorems for C(S)-valued random variables. Zbl 0305.60004
Jain, Naresh C.; Marcus, Michael B.
1975
Integrability of infinite sums of independent vector-valued random variables. Zbl 0318.60036
Jain, Naresh C.; Marcus, Michael B.
1975
Uniform convergence of random Fourier series. Zbl 0317.42008
Marcus, Michael B.
1975
Sufficient conditions for the continuity of stationary Gaussian processes and applications to random series of functions. Zbl 0336.60041
Jain, Naresh C.; Marcus, M. B.
1975
Sufficient conditions for the continuity of stationary Gaussian processes and applications to random series of functions. Zbl 0283.60041
Jain, Naresh C.; Marcus, M. B.
1974
The $$\varepsilon$$-entropy of some compact subsets of l$$^p$$. Zbl 0277.60023
Marcus, M. B.
1974
Asymptotic maxima of continuous Gaussian processes. Zbl 0304.60024
Marcus, M. B.
1974
Inverse functions and integration by parts. Zbl 0285.26008
Boas, R. P. jun.; Marcus, M. B.
1974
Generalizations of Young’s inequality. Zbl 0275.26021
Boas, R. P. jun.; Marcus, M. B.
1974
Sufficient conditions for the continuity of stationary Gaussian processes and applications to random series of functions. Zbl 0275.60053
Jain, Naresh C.; Marcus, M. B.
1974
Continuity of Gaussian processes and random Fourier series. Zbl 0277.60022
Marcus, M. B.
1973
A comparison of continuity conditions for Gaussian processes. Zbl 0265.60039
Marcus, M. B.
1973
Inequalities involving a function and its inverse. Zbl 0235.26009
Boas, R. P. jun.; Marcus, M. B.
1973
A new proof of a sufficient condition for discontinuity of Gaussian processes. Zbl 0257.60015
Jain, N. C.; Marcus, M. B.
1973
Sample behavior of Gaussian processes. Zbl 0379.60040
Marcus, M. B.; Shepp, L. A.
1972
Upper bounds for the asymptotic maxima of continuous Gaussian processes. Zbl 0241.60032
Marcus, M. B.
1972
Gaussian lacunary series and the modulus of continuity for Gaussian processes. Zbl 0222.60026
Marcus, M. B.
1972
Continuity of Gaussian processes. Zbl 0209.49201
Marcus, M. B.; Shepp, L. A.
1970
A bound for the distribution of the maximum of continuous Gaussian processes. Zbl 0234.60054
Marcus, Michael
1970
Hölder conditions for continuous Gaussian processes. Zbl 0255.60027
Marcus, Michael B.
1970
On the domain of attraction of $$e^{-e^{-x}}$$. Zbl 0169.50201
Marcus, Michael; Pinsky, M.
1969
Hölder conditions for Gaussian processes with stationary increments. Zbl 0186.50602
Marcus, M. B.
1968
Gaussian processes with stationary increments possessing discontinuous sample paths. Zbl 0245.60035
Marcus, Michael B.
1968
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#### Cited by 666 Authors

 33 Marcus, Michael B. 23 Rosen, Jay S. 21 Xiao, Yimin 14 Chen, Xia 10 Eisenbaum, Nathalie 10 Samorodnitsky, Gennady Pinkhosovich 9 Giné-Masdéu, Evarist 8 Khoshnevisan, Davar 8 Naor, Assaf 8 Zinn, Joel 7 Lin, Zhengyan 7 Paulauskas, Vygantas Ionovič 7 Rosiński, Jan 6 Albin, J. M. P. 6 Braverman, Michael Sh. 6 Kuelbs, James D. 6 Shao, Qi-Man 5 Adler, Robert Joseph 5 Aurzada, Frank 5 Bass, Richard F. 5 Bourgain, Jean 5 Heinkel, Bernard 5 Junge, Marius 5 Kaspi, Haya 5 Kozachenko, Yuriĭ Vasyl’ovych 5 Le Jan, Yves 5 Li, Wenbo V. 5 Liu, Jingchen 5 Lupu, Titus 5 Nualart, David 5 Pisier, Gilles 5 Shi, Zhan 5 Talagrand, Michel 4 Ait Ouahra, Mohamed 4 Arcones, Miguel A. 4 Basse-O’Connor, Andreas 4 Csáki, Endre 4 Csörgő, Miklós 4 Csörgő, Sándor 4 Ding, Jian 4 Hu, Yaozhong 4 Jain, Naresh C. 4 Kono, Norio 4 Le, Khoa N. 4 Lifshits, Mikhail A. 4 Milman, Vitali D. 4 Norvaiša, Rimas 4 Stelzer, Robert 4 Sznitman, Alain-Sol 4 Tindel, Samy 4 Xu, Gongjun 4 Yang, Xiaochuan 3 Albeverio, Sergio A. 3 Alexander, Kenneth S. 3 Barndorff-Nielsen, Ole Eiler 3 Bednorz, Witold Marek 3 Berman, Simeon M. 3 Biermé, Hermine 3 Bingham, Nicholas Hugh 3 Buldygin, Valeriĭ Volodymyrovych 3 Croydon, David A. 3 Dudley, Richard Mansfield 3 Fernique, Xavier 3 Földes, Antónia 3 Foondun, Mohammud 3 Giuliano Antonini, Rita 3 Hahn, Marjorie Green 3 Heathcote, Christopher R. 3 Imekraz, Rafik 3 Kalinauskaitė, Nijolė Liucija 3 Kwapień, Stanisław 3 Lai, Tze Leung 3 Lee, James R. 3 Lefèvre, Pascal 3 Markowsky, Greg T. 3 Marquardt, Tina 3 Matsak, Ivan K. 3 Meintanis, Simos G. 3 Norvajsha, R. 3 Palazuelos, Carlos 3 Peres, Yuval 3 Račkauskas, Alfredas Yurgevich 3 Révész, Pál 3 Rodríguez-Piazza, Luis 3 Rosalsky, Andrew 3 Rychlik, Igor 3 Schechtman, Gideon 3 Sghir, Aissa 3 Tarrès, Pierre 3 Wang, Wensheng 3 Weber, Michel Jean Georges 3 Welsh, Alan H. 3 Yan, Litan 3 Yuknyavichene, D. B. 3 Zabczyk, Jerzy 3 Zhang, Rongmao 2 Acuña Valverde, Luis 2 Andersen, Niels Toft 2 Astashkin, Sergeĭ Vladimir 2 Benassi, Albert ...and 566 more Authors
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#### Cited in 154 Serials

 90 Stochastic Processes and their Applications 51 The Annals of Probability 33 Statistics & Probability Letters 29 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 28 Probability Theory and Related Fields 24 Journal of Theoretical Probability 21 Journal of Multivariate Analysis 19 Lithuanian Mathematical Journal 18 Transactions of the American Mathematical Society 13 Israel Journal of Mathematics 12 Journal of Functional Analysis 12 The Annals of Applied Probability 10 Journal of Mathematical Analysis and Applications 9 Communications in Mathematical Physics 9 Potential Analysis 9 Bernoulli 8 Ukrainian Mathematical Journal 8 Journal of Statistical Planning and Inference 7 Extremes 6 The Annals of Statistics 6 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 6 Electronic Journal of Probability 4 Mathematical Proceedings of the Cambridge Philosophical Society 4 Annales de l’Institut Fourier 4 Mathematische Annalen 4 Proceedings of the American Mathematical Society 4 Journal of Mathematical Sciences (New York) 4 Annales Mathématiques Blaise Pascal 4 Stochastics 3 Journal of Statistical Physics 3 Acta Mathematica 3 Inventiones Mathematicae 3 Journal of Applied Probability 3 Journal of Approximation Theory 3 Monatshefte für Mathematik 3 Acta Mathematica Hungarica 3 Random Operators and Stochastic Equations 3 Electronic Communications in Probability 3 The Journal of Fourier Analysis and Applications 3 Acta Mathematica Sinica. English Series 3 Methodology and Computing in Applied Probability 3 Stochastics and Dynamics 2 Advances in Applied Probability 2 Bulletin of the Australian Mathematical Society 2 Computers & Mathematics with Applications 2 Journal d’Analyse Mathématique 2 Journal of Mathematical Physics 2 Mathematical Notes 2 Theory of Probability and its Applications 2 Annals of the Institute of Statistical Mathematics 2 Siberian Mathematical Journal 2 Stochastic Analysis and Applications 2 Acta Applicandae Mathematicae 2 Annales de l’Institut Henri Poincaré. Nouvelle Série. Section B. Calcul des Probabilités et Statistique 2 Computational Statistics and Data Analysis 2 Test 2 Applied Mathematics. Series B (English Edition) 2 Theory of Probability and Mathematical Statistics 2 Infinite Dimensional Analysis, Quantum Probability and Related Topics 2 Annals of Mathematics. Second Series 2 Discrete and Continuous Dynamical Systems. Series B 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Electronic Journal of Statistics 2 Modern Stochastics. Theory and Applications 1 Archive for Rational Mechanics and Analysis 1 The Canadian Journal of Statistics 1 Indian Journal of Pure & Applied Mathematics 1 Inverse Problems 1 Metrika 1 Nonlinearity 1 Periodica Mathematica Hungarica 1 Rocky Mountain Journal of Mathematics 1 Scandinavian Journal of Statistics 1 Studia Mathematica 1 Arkiv för Matematik 1 Mathematics of Computation 1 Annales Scientifiques de l’Université de Clermont-Ferrand II. Mathématiques 1 Archiv der Mathematik 1 Bulletin de la Société Mathématique de France 1 Duke Mathematical Journal 1 Indiana University Mathematics Journal 1 Integral Equations and Operator Theory 1 Journal of Computational and Applied Mathematics 1 Journal of Differential Equations 1 Journal of Economic Theory 1 Journal of the London Mathematical Society. Second Series 1 Journal of the Mathematical Society of Japan 1 Journal of Soviet Mathematics 1 Mathematika 1 Memoirs of the American Mathematical Society 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Proceedings of the Japan Academy. Series A 1 Results in Mathematics 1 Statistica Neerlandica 1 Trabajos de Estadistica y de Investigacion Operativa 1 Topology and its Applications 1 European Journal of Combinatorics 1 Rendiconti di Matematica e delle sue Applicazioni. Serie VII 1 Insurance Mathematics & Economics 1 Probability and Mathematical Statistics ...and 54 more Serials
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#### Cited in 47 Fields

 539 Probability theory and stochastic processes (60-XX) 88 Statistics (62-XX) 55 Functional analysis (46-XX) 27 Harmonic analysis on Euclidean spaces (42-XX) 20 Measure and integration (28-XX) 18 Abstract harmonic analysis (43-XX) 17 Numerical analysis (65-XX) 16 Operator theory (47-XX) 14 Partial differential equations (35-XX) 13 Real functions (26-XX) 13 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 11 Combinatorics (05-XX) 11 Statistical mechanics, structure of matter (82-XX) 9 Quantum theory (81-XX) 8 Linear and multilinear algebra; matrix theory (15-XX) 7 Dynamical systems and ergodic theory (37-XX) 6 General topology (54-XX) 6 Computer science (68-XX) 5 Group theory and generalizations (20-XX) 5 Topological groups, Lie groups (22-XX) 5 Functions of a complex variable (30-XX) 5 Information and communication theory, circuits (94-XX) 4 History and biography (01-XX) 4 Convex and discrete geometry (52-XX) 3 Ordinary differential equations (34-XX) 3 Approximations and expansions (41-XX) 3 Integral transforms, operational calculus (44-XX) 2 Mathematical logic and foundations (03-XX) 2 Number theory (11-XX) 2 Potential theory (31-XX) 2 Sequences, series, summability (40-XX) 2 Geometry (51-XX) 2 Differential geometry (53-XX) 2 Algebraic topology (55-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Mechanics of deformable solids (74-XX) 2 Operations research, mathematical programming (90-XX) 2 Biology and other natural sciences (92-XX) 1 Nonassociative rings and algebras (17-XX) 1 Special functions (33-XX) 1 Difference and functional equations (39-XX) 1 Integral equations (45-XX) 1 Manifolds and cell complexes (57-XX) 1 Mechanics of particles and systems (70-XX) 1 Fluid mechanics (76-XX) 1 Geophysics (86-XX) 1 Systems theory; control (93-XX)