The Conditional expectations and the ergodic theorem for strictly stationary generalized stochastic processes

K. Urbanik

Displaying similar documents to “The Conditional expectations and the ergodic theorem for strictly stationary generalized stochastic processes”

Generalized stochastic processes

K. Urbanik (1958)

Studia Mathematica

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Two results on continuity and boundedness of stochastic convolutions

Stanisław Kwapień, Michael B. Marcus, Jan Rosiński (2006)

Annales de l'I.H.P. Probabilités et statistiques

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On the existence and uniqueness of the solution processes in McShane's stochastic integral equation systems

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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Generalized stationary processes of Markovian character

K. Urbanik (1962)

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Testing stationary processes for independence

Gusztáv Morvai, Benjamin Weiss (2011)

Annales de l'I.H.P. Probabilités et statistiques

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Let 0 denote the class of all real valued i.i.d. processes and 1 all other ergodic real valued stationary processes. In spite of the fact that these classes are not countably tight we give a strongly consistent sequential test for distinguishing between them.

Moments of some random functionals

K. Urbanik (1997)

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The paper deals with nonnegative stochastic processes X(t,ω)(t ≤ 0) not identically zero with stationary and independent increments right-continuous sample functions and fulfilling the initial condition X(0,ω)=0. The main aim is to study the moments of the random functionals $\int_{0}^{\infty} f (X (τ, ω)) d τ$ for a wide class of functions f. In particular a characterization of deterministic processes in terms of the exponential moments of these functionals is established.

On the existence, uniqueness and parametric dependence on the coefficients of the solution processes in McShane's stochastic integral equations.

Adrian Constantin (1994)

Publicacions Matemàtiques

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In this paper we use the Schauder fixed point theorem and methods of integral inequalities in order to prove a result on the existence, uniqueness and parametric dependence on the coefficients of the solution processes in McShane stochastic integral equations.