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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André Arnold (1988)
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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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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...