Related papers: Closed-form solutions for the L\'evy-stable distri…
The non-equilibrium steady states emerging from stochastic resetting to a distribution is studied. We show that for a range of processes, the steady-state moments can be expressed as a linear combination of the moments of the distribution…
Statistical systems with time-periodic spatially non-uniform forces are of immense importance in several areas of physics. In this paper, we provide an analytical expression of the time-periodic probability distribution function of…
The sub-Gaussian stable distribution is a heavy-tailed elliptically contoured law which has interesting applications in signal processing and financial mathematics. This work addresses the problem of feasible estimation of distributions. We…
We investigate an example of noise-induced stabilization in the plane that was also considered in (Gawedzki, Herzog, Wehr 2010) and (Birrell, Herzog, Wehr 2011). We show that despite the deterministic system not being globally stable, the…
We derive the generalized Fokker-Planck equation associated with a Langevin equation driven by arbitrary additive white noise. We apply our result to study the distribution of symmetric and asymmetric L\'{e}vy flights in an infinitely deep…
It is demonstrated that any statistics can be represented by an attractor of the solution to a corresponding systen of ODE coupled with its Liouville equation. Such a non-Newtonian representation allows one to reduce foundations of…
We study how the presence of correlations in physical variables contributes to the form of probability distributions. We investigate a process with correlations in the variance generated by (i) a Gaussian or (ii) a truncated L\'{e}vy…
We give a variational formulation of classical statistical mechanics where the one-body density and the local entropy distribution constitute the trial fields. Using Levy's constrained search method it is shown that the grand potential is a…
The mollified uniform distribution is rediscovered, which constitutes a ``soft'' version of the continuous uniform distribution. Important stochastic properties are presented and used to demonstrate potential fields of applications. For…
We provide, in a general setting, explicit solutions for optimal stopping problems that involve diffusion process and its running maximum. Our approach is to use the excursion theory for Levy processes. Since general diffusions are, in…
Let $S_{n}$ be a sum of independent identically distribution random variables with finite first moment and $h_{M}$ be a call function defined by $g_{M}(x)=\max\{x-M,0\}$ for $x\in\mathbb{R}$, $M>0$. In this paper, we assume the random…
We describe the transverse beam distribution in particle accelerators within the controlled, stochastic dynamical scheme of the Stochastic Mechanics (SM) which produces time reversal invariant diffusion processes. This leads to a linearized…
We consider here the recently proposed closed form formula in terms of the Meijer G-functions for the probability density functions $g_\alpha(x)$ of one-sided L\'evy stable distributions with rational index $\alpha=l/k$, with $0<\alpha<1$.…
We derive the exact formula for thermal-equilibrium spacing distribution of one-dimensional particle gas with repulsive potential V(r)=r^(-a) (a>0) depending on the distance r between the neighboring particles. The calculated distribution…
In this paper we present a study of anomalous diffusion using a Fokker-Planck description with fractional velocity derivatives. The distribution functions are found using numerical means for varying degree of fractionality observing the…
The class of $\alpha$-stable distributions received much interest for modelling impulsive phenomena occur in engineering, economics, insurance, and physics. The lack of non-analytical form for probability density function is considered as…
In this paper, we study the cut-off phenomenon under the total variation distance of $d$-dimensional Ornstein-Uhlenbeck processes which are driven by L\'evy processes. That is to say, under the total variation distance, there is an abrupt…
The distributional support of the sample paths of L\'evy processes is an important issue for the construction of sparse statistical models, theories of integration in infinite dimensions and the existence of generalized solutions of…
We present results of the numerical simulations and the scaling characteristics of one-dimensional random fluctuations with heavy tailed probability distribution functions. Assuming that the distribution function of the random fluctuations…
The study of distributed order calculus usually concerns about fractional derivatives of the form $\int_0^1 \partial^\alpha u \, m(d\alpha)$ for some measure $m$, eventually a probability measure. In this paper an approach based on L\'evy…