Bessel and Volatility-Stabilized Processes

We present a Matlab program that computes infinite range integrals of an arbitrary product of Bessel functions of the first kind. The algorithm uses an integral representation of the upper incomplete Gamma function to integrate the tail of the integrand. This paper describes the algorithm and then focuses on some implementation aspects of the Matlab program. Finally we mention a generalisation ...

We formulate a refined version of the global Gan–Gross–Prasad conjecture for general Bessel models, extending the work of Ichino–Ikeda and R. N. Harris in the co-rank 1 case. It is an explicit formula relating the automorphic period of Bessel type and the central value of certain L-function. To support such conjecture, we provide two examples for pairs SO5 SO2 and SO6 SO3 (both co-rank 3) in th...

Change in impedance of an encircling coil is obtained in the present paper for the case where the electric conductivity and magnetic permeability of a metal cylindrical tube depend on the radial coordinate. The system of equations for the vector potential is solved by means of the Fourier cosine transform. The solution is expressed in terms of improper integral containing modified Bessel functi...

The problems of wave diffraction by a plane angular screen occupying an infinite 45 degree wedge sector with Dirichlet and/or Neumann boundary conditions are studied in Bessel potential spaces. Existence and uniqueness results are proved in such a framework. The solutions are provided for the spaces in consideration, and higher regularity of solutions are also obtained in a scale of Bessel pote...

Some novel interlacing properties of the zeros for the Bessel and spherical Bessel functions are first presented and then applied to prove an interesting uniqueness result in inverse acoustic obstacle scattering. It is shown that in the resonance region, the shape of a sound-soft/sound-hard ball in R3 or a soundsoft/sound-hard disc in R2 is uniquely determined by a single far-field datum measur...