We show that if (Xs, s ≥ 0) is a right-continuous process, Yt = ∫ t 0 dsXs its integral process and τ = (τl, l ≥ 0) a subordinator, then the time-changed process (Yτl , l ≥ 0) allows to retrieve the information about (Xτl , l ≥ 0) when τ is stable, but not when τ is a gamma subordinator. This question has been motivated by a striking identity in law involving the Bessel clock taken at an indepe...

The pseudodifferential operator (p.d.o.)A(x,D), associated with the Bessel operator d2/dx2 + (1− 4μ2)/4x2, is defined. Symbol class Hm ρ,δ is introduced. It is shown that the p.d.o. associated with a symbol belonging to this class is a continuous linear mapping of the Zemanian spaceHμ into itself. An integral representation of p.d.o. is obtained. Using Hankel convolution Lσ,α-norm continuity of...

We construct an example of a Hölder continuous vector field on the plane which is tangent to all foliations in a continuous family of pairwise distinct C foliations. Given any 1 ≤ r < ∞, the construction can be done in such a way that each leaf of each foliation is the graph of a Cr function from R to R. We also show the existence of a continuous vector field X on R and two foliations F and G o...

We present a space-time generalization of the known spatial (monochromatic) wave vortex beams carrying intrinsic orbital angular momentum (OAM) along the propagation direction. Generic spatiotemporal vortex beams are polychromatic and can carry intrinsic OAM at an arbitrary angle to the mean momentum. Applying either (i) a transverse wave-vector shift or (ii) a Lorentz boost to a monochromatic ...

We provide a new mathematical technique leading to the construction of the exact parametric or closed form solutions of the classes of Abel’s nonlinear differential equations ODEs of the first kind. These solutions are given implicitly in terms of Bessel functions of the first and the second kind Neumann functions , as well as of the free member of the considered ODE; the parameter ν being intr...

We relate the formulas giving Brownian (and other) intersection exponents to the absolute continuity relations between Bessel process of different dimensions, via the two-parameter family of SchrammLoewner Evolution processes SLE(03BA, p) introduced in [23]. This allows us also to compute the value of some new exponents ( "hiding exponents" ) related to SLEs, planar Brownian motions and the con...

Based on the generalized multiparticle Mie theory, multiple scattering of an aggregate of uniaxial anisotropic spheres illuminated by a zero-order Bessel beam (ZOBB) with arbitrary propagation direction is investigated. The particle size and configuration are arbitrary. The arbitrary incident Bessel beam is expanded in terms of spherical vector wave functions (SVWFs). Utilizing the vector addit...

We propose a new generator of continuous distributions, so called the transmuted generalized odd exponential-G family, which extends family introduced by Alizadeh et al. (2017). Some statistical properties such as; raw and incomplete moments, moment generating function, Lorenz Bonferroni curves, probability weighted Rényi entropy, stress strength model order statistics are investigated. The par...