Displaying similar documents to “Operator self-similar processes on Banach spaces.”

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

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...

Small deviations of iterated processes in the space of trajectories

Andrei Frolov (2013)

Open Mathematics

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We derive logarithmic asymptotics of probabilities of small deviations for iterated processes in the space of trajectories. We find conditions under which these asymptotics coincide with those of processes generating iterated processes. When these conditions fail the asymptotics are quite different.

On the Structure of Spatial Branching Processes

Matthes, Klaus, Nawrotzki, Kurt, Siegmund-Schultze, Rainer (1997)

Serdica Mathematical Journal

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The paper is a contribution to the theory of branching processes with discrete time and a general phase space in the sense of [2]. We characterize the class of regular, i.e. in a sense sufficiently random, branching processes (Φk) k∈Z by almost sure properties of their realizations without making any assumptions about stationarity or existence of moments. This enables us to classify the clans of (Φk) into the regular part and the completely non-regular part. It turns out that the...