Displaying similar documents to “Analytic stochastic processes”

Induced stationary process and structure of locally square integrable periodically correlated processes

Andrzej Makagon (1999)

Studia Mathematica

Similarity:

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...

Equations in differentials in the algebra of generalized stochastic processes

Nadzeya V. Bedziuk, Aleh L. Yablonski (2010)

Banach Center Publications

Similarity:

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...