Related papers: A Fractional Hawkes process
We prove that the operator $L_0=-(1+|x|)^\beta(-\Delta)^{\alpha/2}$ with $\alpha\in(0,2)$, $d>\alpha$ and $\beta\ge0$ generates a compact semigroup or resolvent on $L^2(\R^d;(1+|x|)^{-\beta}\,dx)$, if and only if $\beta>\alpha$. When…
The rare decays $\eta^{(\prime)}\to\ell^+\ell^-$, $\ell\in\{e,\mu\}$, are highly suppressed in the Standard Model, both by their chirality structure and the required loop attaching the lepton line to the $\eta^{(\prime)}\to\gamma^*\gamma^*$…
A kinetic equation for Compton scattering is given that differs from the Kompaneets equation in several significant ways. By using an inverse differential operator this equation allows treatment of problems for which the radiation field…
We perform a detailed analysis of thermal leptogenesis in the framework of seesaw models which approximately conserve lepton number. These models are known to allow for large Yukawa couplings and a low seesaw scale in agreement with…
We prove a law of large numbers and functional central limit theorem for a class of multivariate Hawkes processes with time-dependent reproduction rate. We address the difficulties induced by the use of non-convolutive Volterra processes by…
We give a direct proof of fractional Hardy inequality by means of Littlewood-Paley decomposition and properties of singular homogeneous kernels of degree -$d$. A refinement when $q>2$ is proved.
In this work, we introduce a new process by modifying the kernel in the time domain representation of the generalized Hermite process. This modification is constructed by means of multiplication of the kernel in the time definition of the…
Hawkes Processes are a type of point process for modeling self-excitation, i.e., when the occurrence of an event makes future events more likely to occur. The corresponding self-triggering function of this type of process may be inferred…
The Mittag-Leffler function is universally acclaimed as the Queen function of fractional calculus. The aim of this work is to survey the key results and applications emerging from the three-parameter generalization of this function, known…
In this paper, we consider the backward problem for fractional in time evolution equations $\partial_t^\alpha u(t)= A u(t)$ with the Caputo derivative of order $0<\alpha \le 1$, where $A$ is a self-adjoint and bounded above operator on a…
Motivated by the study of relativistic atoms, we consider the Hardy operator $(-\Delta)^{\alpha/2}-\kappa|x|^{-\alpha}$ acting on functions of the form $u(|x|) |x|^{\ell} Y_{\ell,m}(x/|x|)$ in $L^2(\mathbb{R}^d)$, when $\kappa\geq0$ and…
Most generalized fractional operators rely on prescribed memory kernels, restricting hereditary behavior to predefined forms and limiting flexibility in modeling diverse memory effects. Motivated by these limitations, this paper develops a…
This article is devoted to derivation of the Laplace transforms of the derivatives with respect to parameters of certain special functions, namely, the Mittag-Leffler type, Wright and Le Roy type functions. These formulas show…
We consider a Stokes-Magneto system in $\mathbb{R}^d$ ($d\geq 2$) with fractional diffusions $\Lambda^{2\alpha}\boldsymbol{u}$ and $\Lambda^{2\beta}\boldsymbol{b}$ for the velocity $\boldsymbol{u}$ and the magnetic field $\boldsymbol{b}$,…
Due to its clustering and self-exciting properties, the Hawkes process has been used extensively in numerous fields ranging from sismology to finance. Since data is often aquired on regular time intervals, we propose a piece-wise constant…
In this paper, we propose a solution of fractional logistic equation by using properties of Mittag-Leffler function.
By transforming the Zeta function into a real function through Laplace inverse transformation, an algebraic research paradigm for prime number distribution was established, and important results were obtained (page 10). This method has…
We have computed the electroweak corrections to $H\rightarrow Z\,Z^*\rightarrow$ 4 charged leptons, including the effect of anomalous $HHH$ coupling in the $\kappa$-framework. The results of this scaling are gauge invariant. We have…
We compute the energy spectrum of charged leptons in the decay $H^+\to \bar b+(t\to bl\nu_l)$. The shape of the lepton spectrum obtained, and also the mean lepton energy, are sensitive to the handedness of the intermediate top quark. This…
A form of the Laplace transform is reviewed as a paradigm for an entire class of fractional functional transforms. Various of its properties are discussed. Such transformations should be useful in application to differential/integral…