‎in this paper‎, ‎first we develop the duality concept for $g$-bessel sequences‎ ‎and bessel fusion sequences in hilbert spaces‎. ‎we obtain some results about dual‎, ‎pseudo-dual ‎and approximate dual of frames and fusion frames‎. ‎we also expand every $g$-bessel ‎sequence to a frame by summing some elements‎. ‎we define the restricted isometry property for ‎$g$-frames and generalize some resu...

We obtain a closed-form solution for the double-Laplace transform of Asian options under the hyper-exponential jump diffusion model (HEM). Similar results are only available previously in the special case of the Black-Scholes model (BSM). Even in the case of the BSM, our approach is simpler as we essentially use only Itô’s formula and do not need more advanced results such as those of Bessel pr...

The intensity statistics of random signals in the presence of Gaussian noise is obtained by considering the model of a random signal plus a random phasor sum. The additive Gaussian noise is shown to result in a Bessel transform of the probability density of signal intensity. The transformation of the intensity statistics can generally be applied to mixtures of independent random signals, one of...

The present paper provides exact expressions for the probability distribution of linear functionals of the two–parameter Poisson–Dirichlet process PD(α, θ). Distributional results that follow from the application of an inversion formula for a (generalized) Cauchy– Stieltjes transform are achieved. Moreover, several interesting integral identities are obtained by exploiting a correspondence betw...

The Constant Elasticity of Variance (CEV) model is mathematically presented and then used in a Credit-Equity hybrid framework. Next, we propose extensions to the CEV model with default: firstly by adding a stochastic volatility diffusion uncorrelated from the stock price process, then by more generally time changing Bessel processes and finally by correlating stochastic volatility moves to the ...

We study the Fourier transform of polynomials in an orthogonal family, taken with respect to the orthogonality measure. Mastering the asymptotic properties of these transforms, that we call Fourier–Bessel functions, in the argument, the order, and in certain combinations of the two is required to solve a number of problems arising in quantum mechanics. We present known results, new approaches a...

The classical theory of Gaussian quadrature assumes a positive weight function. We will show that in some cases Gaussian rules can be constructed with respect to an oscillatory weight, yielding methods with complex quadrature nodes and positive weights. These rules are well suited for highly oscillatory integrals because they attain optimal asymptotic order. We show that for the Fourier oscilla...

A Bessel beam optical trap is combined with continuous wave cavity ringdown spectroscopy to measure the extinction cross section of individual aerosol particles. Particles, ∼1 μm in size, can be captured indefinitely and processes that transform size or refractive index studied. The measured light extinction induced by the particle is shown to depend on the position of the particle in the cavit...

In this paper, we study some basic analytic properties of the boundary term of Fesenko’s two-dimensional zeta integrals. In the case of the rational number field, we show that this term is the Laplace transform of certain infinite series consisting of K-Bessel functions. It is known that the non-positivity property of the fourth log derivative of such series is a sufficient condition for the Ri...