Let be a stochastically continuous, separable, Gaussian process with . A sufficient condition, in terms of the monotone rearrangement of , is obtained for 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.
Si considera, sul gruppo degli interi, una passeggiata aleatoria uscente dall’origine, i cui passi ammettano due soli possibili valori: uno strettamente negativo, l’altro strettamente positivo. Nel caso particolare in cui il primo di questi valori sia , si dà un’espressione esplicita per la legge del primo istante di ritorno nell’origine.
We introduce the sum of observables in fuzzy quantum spaces which generalize the Kolmogorov probability space using the ideas of fuzzy set theory.
In this paper we get some results about the asymptotic behaviour of the sequenceΠn = 1 + X1 + X1X2 + X1X2X3 + ...where {Xn}n=1∞ are i.i.d. random variables. Strong limit laws, Central limit theorem and Iterated Logarithm law are obtained, after an analysis of the convergence of Πn. Rates of convergence are also given.
* Research supported by NATO GRANT CRG 900 798 and by Humboldt Award for U.S. Scientists.In this paper a general theory of a random number of random variables is constructed. A description of all random variables ν admitting an analog of the Gaussian distribution under ν-summation, that is, the summation of a random number ν of random terms, is given. The v-infinitely divisible distributions are described for these ν-summations and finite estimates of the approximation of ν-sum distributions with...
Erdős and Rényi proposed in 1960 a probabilistic model for sums of s integral sth powers. Their model leads almost surely to a positive density for sums of s pseudo sth powers, which does not reflect the case of sums of two squares. We refine their model by adding arithmetical considerations and show that our model is in accordance with a zero density for sums of two pseudo-squares and a positive density for sums of s pseudo sth powers when s ≥ 3. Moreover, our approach supports a conjecture of...