It is shown that the tail probability of a Bessel process is the distributio function of a random time which is related to first and last passage times of Bessel processes. AMS Classification 60 J 25, 60 J 60, 60 E 15, 60 G 44, 60 H 10.

Delest, M. In this paper, we show that the generating function for skew Ferrers diagrams according to their width and area is the quotient of new basic Bessel functions. Nous montrons dans cet article que la fonction g&ntratrice des diagrammes de Ferrers gauches selon les paramktres ptrimttre et aire s'exprime en fonction du quotient des q analogues de deux fonctions de Bessel.

In a previous study, we discussed the expansion of two-parameter functions in a double series of Chebyshev polynomials, and, in particular, we presented coefficients for the evaluation of the modified Bessel function (2z I iifne'K,(z) to 20 decimals for all z ^ 5 and all v, 0 g v g 1. In the present study, we give similar coefficients for the evaluation of ge~'z-»l,(z) to at least 20 decimals w...

In this paper we show that any shift-invariant Bessel sequence with an at most countable number of generators can be extended to a tight frame for its closed linear span by adding another shift-invariant system with at most the same number of generators. We show that in general this result is optimal, by providing examples where it is impossible to obtain a tight frame by adding a smaller numbe...

The notion of frame in a Banach spaces E via semi-inner product was introduced and studied in [16]. In this paper, we give a characterisation for SIP-II Ed-Bessel sequence to be SIP-II Ed-frame. Also, a necessary and sufficient condition for the finite sum of SIP-II Ed frame for E to be a SIP-II Ed frame for E has been obtained. Further, a sufficient condition for the stability of finite sum of...

We address Bessel optical lattices of radial symmetry imprinted in cubic Kerr-type nonlinear media and show that they support families of stable dipole-mode solitons featuring two out-of-phase light spots located in different lattice rings. We show that the radial symmetry of the Bessel lattices affords a variety of unique soliton dynamics including controlled radiation-free rotation of the dip...

The purpose of the present paper is to derive the necessary and sufficient condition for the generalized Bessel function (struve function) belonging to the classes Ωλ(g;α, β) and Υ ∗ λ(g;α, β).

In this paper, we study approximate duals of $g$-frames and fusion frames in Hilbert $C^ast-$modules. We get some relations between approximate duals of $g$-frames and biorthogonal Bessel sequences, and using these relations, some results for approximate duals of modular Riesz bases and fusion frames are obtained. Moreover, we generalize the concept of $Q-$approximate duality of $g$-frames and ...