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Groups with small deviation for non-subnormal subgroups

100%

Kurdachenko L., Smith H.

Open Mathematics

2009

tom 7

nr 2

186-199

We introduce the notion of the non-subnormal deviation of a group G. If the deviation is 0 then G satisfies the minimal condition for nonsubnormal subgroups, while if the deviation is at most 1 then G satisfies the so-called weak minimal condition for such subgroups (though the converse does not hold). Here we present some results on groups G that are either soluble or locally nilpotent and that have deviation at most 1. For example, a torsion-free locally nilpotent with deviation at most 1 is nilpotent, while a Baer group with deviation at most 1 has all of its subgroups subnormal.

Karhunen-Loève expansions of α-Wiener bridges

61%

Barczy M., Iglói E.

Open Mathematics

2011

tom 9

nr 1

65-84

We study Karhunen-Loève expansions of the process(X t(α))t∈[0,T) given by the stochastic differential equation $$ dX_t^{(\alpha )} = - \frac{\alpha } {{T - t}}X_t^{(\alpha )} dt + dB_t ,t \in [0,T) $$, with the initial condition X 0(α) = 0, where α > 0, T ∈ (0, ∞), and (B t)t≥0 is a standard Wiener process. This process is called an α-Wiener bridge or a scaled Brownian bridge, and in the special case of α = 1 the usual Wiener bridge. We present weighted and unweighted Karhunen-Loève expansions of X (α). As applications, we calculate the Laplace transform and the distribution function of the L 2[0, T]-norm square of X (α) studying also its asymptotic behavior (large and small deviation).

Ograniczanie wyników

2 Open Mathematics

1 Barczy M.

1 Iglói E.

1 Kurdachenko L.

1 Smith H.

1 2011

1 2009

Wyniki wyszukiwania

Groups with small deviation for non-subnormal subgroups

Karhunen-Loève expansions of α-Wiener bridges