We study a problem of optimal consumption and portfolio selection in a market where the logreturns of the uncertain assets are not necessarily normally distributed. The natural models then involve pure-jump L evy processes as driving noise instead of Brownian motion like in the Black and Scholes model. The state constrained optimization problem involves the notion of local substitution and is o...

We study the possible interpretation of "universal constants" by classification J.~M.~L\'evy-Leblond. $\hbar$ and $c$ are most common example constants this type. Using Fock's principle relativity w.r.t. observation means, we show that both can be viewed as manifestations certain relativity. also there is a possibility to interpret Boltzmann's constant in similar way, make some comments about r...

We explore the behavior of power-law shot noise, for which the associated impulse response functions assume a decaying power-law form. We obtain expressions for the moments, moment generating functions, amplitude probability density functions, autocorrelation functions, and power spectral densities for a variety of parameters of the process. For certain parameters the power spectral density exh...

The innnitely divisible distributions on R + of random variables C t , S t and T t with Laplace transforms 1 cosh p 2 t ; p 2 sinh p 2 ! t ; and tanh p 2 p 2 ! t respectively are characterized for various t > 0 in a number of diierent ways: by simple relations between their moments and cumulants, by corresponding relations between the distributions and their L evy measures, by recursions for th...

Using a hydrodynamic approach, we show that charge diffusion in two dimensional Coulomb interacting liquids with broken momentum conservation is intrinsically anomalous. The relaxation governed by an overdamped, superdiffusive plasmon mode. We demonstrate the diffusing particles follow L\'evy flight trajectories, and study collective modes under influence of magnetic fields. latter are shown to...

We revisit Merton’s portfolio optimization problem under bounded state-dependent utility functions, in a market driven by a Lévy process Z extending results by Karatzas et. al. [8] and Kunita [11]. The problem is solved using a dual variational problem as it is customarily done for nonMarkovian models. One of the main features here is that the domain of the dual problem enjoys an explicit “para...

A new basis has been found for the theory of self-organization transport avalanches and jet zonal flows in L-mode tokamak plasma, so-called "plasma staircase." The are considered as a wave packet coupled nonlinear oscillators characterized by complex time- wave-number dependent function; mean-field approximation this function is argued to obey discrete Schr\"odinger equation with subquadratic p...

The measurement of two-particle Bose-Einstein momentum correlation functions are presented using $\sqrt{s_{_{\text{NN}}}}=5.02$ TeV PbPb collision data, recorded by the CMS experiment in 2018. measured discussed terms L\'evy type source distributions. parameters extracted as transverse mass and centrality. These include strength $\lambda$, stability index $\alpha$, scale parameter $R$. shape, c...