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A central limit theorem for strictly stationary sequences in terms of slow variation in the limit

100%

Szewczak Z. S.

Probability and Mathematical Statistics

1998

tom Vol. 18, Fasc. 2

359--368

For strictly stationary random sequences satisfying the “minimal” dependence condition, necessary and sufficient conditions for the weak convergence to the normal law in terms of slow variation in the limit are found.

Diffusion limits for the queue length of jobs in multi-server open queueing networks

80%

Greičius E. , Minkevičius S.

tom Vol. 27, No. 4

71--84

A mathematical model of a multiserver open queueing network in heavy traffic is developed. This model is that of a multiserver computer system network in heavy traffic. A limit theorem for the length of the queue has been presented.

A limit theorem for the last exit time over a moving nonlinear boundary for a Gaussian process

70%

Karagodin N.

tom Vol. 42, Fasc. 2

195--217

We prove the convergence of the distribution of the scaled last exit time over a slowly moving nonlinear boundary for a class of Gaussian stationary processes. The limit is a double exponential (Gumbel) distribution.

On the local time of multiparameter symmmetric stable processes. Regularity and limit theorem in Besov spaces

60%

Boufoussi B. , Dozzi M.

Probability and Mathematical Statistics

2003

tom Vol. 23, Fasc. 2

369--387

Let X = (Xz, z ϵ TN = [0, l]N) be a symmetric α-stable process, 1 < α ≤ 2. Based on a Kolmogorov type continuity theorem we show Hölder conditions in Lp-norms for the local time of X with respect to the space and time variables, by distinguishing the cases where the time variables do or do not meet the axes. Weak convergence of the occupation integral is proved.

Extremes of multidimensional stationary Gaussian random fields

60%

Soja-Kukieła N.

tom Vol. 38, Fasc. 1

191--207

Let {X(t) : t = (t1, t2,…, td) ϵ [0, ∞)d} be a centered stationary Gaussian field with almost surely continuous sample paths, unit variance and correlation function r satisfying r(t) < 1 for every t ≠ 0 and r(t) = 1 – Σdi=1 |ti|αi + o (Σdi=1 |ti|αi), as t → 0, with some α1, α2,…, αd ϵ (0, 2]. The main result of this contribution is the description of the asymptotic behaviour of P (sup{X(t) : t ϵ Jxm} ≤ u), as u → ∞, for some Jordan-measurable sets Jxm of volume proportional to P (sup{X(t) : t ϵ [0, 1]d} > u)−1 (1 + o(1)).

Unconditional convergence in lattice groups with respect to ideals

60%

Boccuto A. , Dimitriou X. , Papanastassiou N.

tom Vol. 50, [Z] 2

161-174

We deal with unconditional convergence of series and some special classes of subsets of N.