Abstract
Variance mixtures of the normal distribution with infinitely divisible mixing measures and a class G of stochastic processes, which naturally arises from such distributions, are studied.
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References
Borell, C. (1974). Convex measures on locally convex spaces. Arkiv Mat. 12, 239–252.
Feller, W. An introduction to probability theory and its applications. Volume II. First ed. J. Wiley & Sons, New York, 1966.
Kallenberg, O. (1973). Series of random processes without discontinuities of the second kind. Ann. Probab. 2, 729–737.
Kelker, D. (1971). Infinite divisibility and variance mixtures of the normal distribution. Ann. Math. Statist. 42, 802–808.
Lau, Ka-Sing and Rao, C. Radhakrishna (1984). Solution to the integrated Cauchy functional equation on the whole line. Sankhyā A 46, 311–318.
LePage, R. (1980). Multidimensional infinitely divisible variables and processes. Part I: Stable case. Technical report no. 292. Dept. of Statistics, Stanford University.
Marcus, M. B. (1987). ξ-radial processes and random Fourier series. Memoirs Amer. Math. Soc. 368.
Marcus, M. B. and Pisier, G. (1984). Characterizations of almost surely continuous p-stable random Fourier series and strongly stationary processes. Acta Math. 152, 245–301.
Maruyama, G. (1970). Infinitely divisible processes. Theor. Prob. Appl. 15, 3–23.
Rajput, B. S. (1977). On the support of symmetric infinitely divisible and stable probability measures on LCTVS. Proc. Amer. Math. Soc. 66, 331–334.
Rosinski, J. (1990). On series representations of infinitely divisible random vectors. Ann. Probab. 18, 405–430.
Rosinski, J. (1990). An application of series representations for zero-one laws for infinitely divisible random vectors. Probability in Banach Spaces 7, Progress in Probability 21, Birkhauser, 189–199.
Steutel, F. W. (1979). Infinite divisibility in theory and practice. Scand. J. Statist. 6, 57–64.
Sztencel, R. (1986). Absolute continuity of the lower tail of stable seminorms. Bull. Pol. Acad. Sci. Math. 34, 231–234.
Talagrand, M. (1988). Necessary conditions for sample boundedness of p-stable processes. Ann. Probab. 16, 1584–1595.
Urbanik, K. and Woyczynski, W. A. (1967). Random integrals and Orlicz spaces. Bull. Acad. Polon. Sci. 15, 161 –169.
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© 1991 Birkhäuser Boston
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Rosinski, J. (1991). On A Class of Infinitely Divisible Processes Represented as Mixtures of Gaussian Processes. In: Cambanis, S., Samorodnitsky, G., Taqqu, M.S. (eds) Stable Processes and Related Topics. Progress in Probabilty, vol 25. Birkhäuser Boston. https://doi.org/10.1007/978-1-4684-6778-9_2
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DOI: https://doi.org/10.1007/978-1-4684-6778-9_2
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4684-6780-2
Online ISBN: 978-1-4684-6778-9
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