Hilbert-space of a class of multidimensional stochastic processes
T. K. Pogany (1989)
Matematički Vesnik
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T. K. Pogany (1989)
Matematički Vesnik
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K. Urbanik (1958)
Studia Mathematica
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M. M. Sysło (1974)
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André Arnold (1988)
Banach Center Publications
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Swift, Randall J. (2000)
Portugaliae Mathematica
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Andrzej Makagon (1999)
Studia Mathematica
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A one-to-one correspondence between locally square integrable periodically correlated (PC) processes and a certain class of infinite-dimensional stationary processes is obtained. The correspondence complements and clarifies Gladyshev's known result [3] describing the correlation function of a continuous periodically correlated process. In contrast to Gladyshev's paper, the procedure for explicit reconstruction of one process from the other is provided. A representation of a PC process...
B. Kopociński (1966)
Applicationes Mathematicae
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J. M. Angulo Ibáñez, R. Gutiérrez Jáimez (1988)
Annales scientifiques de l'Université de Clermont-Ferrand 2. Série Probabilités et applications
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A. Plucińska (1971)
Applicationes Mathematicae
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Martin T. Barlow, Peter Imkeller (1992)
Séminaire de probabilités de Strasbourg
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Kunze, M., Monteiro Marques, Manuel D.P. (1997)
Journal of Convex Analysis
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Nadzeya V. Bedziuk, Aleh L. Yablonski (2010)
Banach Center Publications
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We consider an ordinary or stochastic nonlinear equation with generalized coefficients as an equation in differentials in the algebra of new generalized functions in the sense of [8]. Consequently, the solution of such an equation is a new generalized function. We formulate conditions under which the solution of a given equation in the algebra of new generalized functions is associated with an ordinary function or process. Moreover the class of all possible associated functions and processes...