Using an extension of the Cox-Ingersoll-Ross [1] stochastic model of the short interest rate r, we study the convergence in law of the longterm return in order to make some approximations. We use the theory of Bessel processes and observe the convergence in law of the sequence (√ −2β3 δn ∫ nt 0 (Xu + δu 2β )du ) t≥0 with the X a generalized Besselsquare process with drift with stochastic revers...

in this paper we introduce a new definition of the first non-abelian cohomology of topological groups.  we relate the cohomology of a normal subgroup $n$ of a topological group $g$ and the quotient $g/n$ to the cohomology of $g$. we get the inflation-restriction exact sequence. also, we obtain a seven-term exact cohomology sequence up to dimension 2. we give an interpretation of the first non-a...

Introduction. Whittaker models have been crucial in the development of the theory of automorphic forms. Within the Langlands-Shahidi method, Whittaker models give rise to the definition of local coefficients [Sh1,Sh2], which proved critical in establishing the proof of Langlands’s conjecture relating local L–functions to Plancherel measures for generic representations [Sh3]. This, in turn, led ...

The theory of localized frames is a recently introduced concept with broad implications to frame theory in general, as well as to the special cases of Gabor and wavelet frames. Using the new notion of a R-dual sequence associated with a Bessel sequence, we derive several duality principles concerning localization in abstract frame theory. As applications of our results we prove a duality princi...

Light scattered by turbid tissue is known to degrade optical coherence tomography (OCT) image contrast progressively with depth. Bessel beams have been proposed as an alternative to Gaussian beams to image deeper into turbid tissue. However, studies of turbid tissue comparing the image quality for different beam types are lacking. We present such a study, using numerically simulated beams and e...

We give two distinct approaches to finding bounds, as functions of the order ν, for the smallest real or purely imaginary zero of Bessel and some related functions. One approach is based on an old method due to Euler, Rayleigh, and others for evaluating the real zeros of the Bessel function Jν(x) when ν > −1. Here, among other things, we extend this method to get bounds for the two purely imagi...

In this paper the asymptotic behavior of an unstable integer-valued autoregressive model of order p (INAR(p)) is described. Under a natural assumption it is proved that the sequence of appropriately scaled random step functions formed from an unstable INAR(p) process converges weakly towards a squared Bessel process. We note that this limit behavior is quite different from that of familiar unst...

We study the existence and uniqueness of solutions of SDEs describing squared Bessel particle systems in full generality. We define non-negative and non-colliding squared Bessel particle systems and we study their properties. Particle systems dissatisfying noncolliding and unicity properties are pointed out. The structure of squared Bessel particle systems is described.

We consider a class of functions, defined on a locally compact abelian group by letting a class of modulation operators act on a countable collection of functions. We derive sufficient conditions for such a class of functions to form a Bessel sequence or a frame and for two such systems to be dual frames. Explicit constructions are obtained via various generalizations of the classical B-splines...