Displaying similar documents to “Asymptotic normality of eigenvalues of random ordinary differential operators”

Sufficient conditions for the continuity of stationary gaussian processes and applications to random series of functions

Naresh C. Jain, Michael B. Marcus (1974)

Annales de l'institut Fourier

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Let { X ( t ) , t ∈ [ 0 , 1 ] n } be a stochastically continuous, separable, Gaussian process with E [ X ( t + h ) - X ( t ) ] 2 = σ 2 ( | h | ) . A sufficient condition, in terms of the monotone rearrangement of σ , is obtained for X ( t ) to have continuous sample paths almost surely. This result is applied to a wide class of random series of functions, in particular, to random Fourier series.

Moments of some random functionals

K. Urbanik (1997)

Colloquium Mathematicum

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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 ∫ 0 ∞ 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 density of some Wiener functionals: an application of Malliavin calculus.

Antoni Sintes Blanc (1992)

Publicacions Matemàtiques

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Using a representation as an infinite linear combination of chi-square independent random variables, it is shown that some Wiener functionals, appearing in empirical characteristic process asymptotic theory, have densities which are tempered in the properly infinite case and exponentially decaying in the finite case.