Abstract In this paper we derive martingale estimating functions for the dimensionality parameter of a Bessel process based on eigenfunctions diffusion operator. Since is non-ergodic and theory developed ergodic diffusions, use space-time transformation formulate our results modified process. We deduce consistency, asymptotic normality discuss optimality. It turns out that function first eigenf...

This paper presents novel analytic expressions for the Rice Ie−function, Ie(k, x), and the incomplete Lipschitz-Hankel Integrals (ILHIs) of the modified Bessel function of the first kind, Iem,n(a, z). Firstly, an exact infinite series and an accurate polynomial approximation are derived for the Ie(k, x) function which are valid for all values of k. Secondly, an exact closed-form expression is d...

Some new properties of kernels of modified Kontorovitch–Lebedev integral transforms — modified Bessel functions of the second kind with complex orderK 1 2+iβ (x) are presented. Inequalities giving estimations for these functions with argument x and parameter β are obtained. The polynomial approximations of these functions as a solutions of linear differential equations with polynomial coefficie...

Infinite integrals involving Bessel functions are recast, by means of an Abel transform, in terms of Fourier integrals. As there are many efficient numerical methods for computing Fourier integrals, this leads to a convenient way of approximating Bessel function integrals.