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In this note, we recall main properties of generalized random fields and present a proof of the continuity theorem of Paul L\'evy for generalized random fields in the space of tempered distributions.
Generalized random processes
Gel ′ · 1955
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Generalized random processes and their extension in measure
Minlos, R. A. (1959) · 1959
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Generalized functions. Vol. 4
Gel ′ · 1964
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Topological vector spaces, distributions and kernels
Trèves, F. (1967) · 1967
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Généralisations du théorème de continuité de P. Lévy
Fernique, X. (1968) · 1968
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Generalized functions. Vol. 2. Spaces of fundamental and generalized functions
Gel ′ · 1968
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Quantum fields and Markoff fields
Nelson, E. (1973) · 1971
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Convergence cylindrique et convergence étroite d’une suite de probabilités de Radon
Boulicaut, P. (1973/74) · 1973
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A study of the properties of generalized Gaussian random fields
Dobrušin, R. L. and Minlos, R. A. (1976) · 1976
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Generalized Ornstein-Uhlenbeck processes and infinite particle branching Brownian motions
Holley, R. A. and Stroock, D. W. (1978) · 1978
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Methods of modern mathematical physics. I
Reed, M. and Simon, B. (1980) · 1980
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Distribution-valued processes arising from independent Brownian motions
Itô, K. (1983) · 1983
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Harmonic analysis on semigroups
Berg, C., Christensen, J. P. R., and Ressel, P. (1984) · 1984
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Stochastic differential equations in infinite-dimensional spaces
Kallianpur, G. and Xiong, J. (1995) · 1995
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Le théorème de continuité de P. Lévy sur les espaces nucléaires (d’après X. Fernique)
Meyer, P.-A. (1995) · 1995
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White noise distribution theory
Kuo, H.-H. (1996) · 1996
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Foundations of modern probability
Kallenberg, O. (1997) · 1997
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On the continuity of characteristic functionals and sparse stochastic modeling
Fageot, J., Amini, A., and Unser, M. (2014) · 2014
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Wavelet statistics of sparse and self-similar images
Fageot, J., Bostan, E., and Unser, M. (2015) · 2015
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Nuclear Gel ′
Gorostiza, L. G. and Nualart, D. (1994) · 1994
Cited alongside, same era.