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We investigate approximating joint distributions of random processes with causal dependence tree distributions. Such distributions are particularly useful in providing parsimonious representation when there exists causal dynamics among…
The multiplier statistics of discrete and continuous nonconservative multiplicative cascade models, employed to describe the energy cascade in fully developed turbulence, is investigated. It is found to be indistinguishable due to…
In this paper the generalization of the Poisson distribution is derived for the case when each consecutive event changes event rate. A simple formula for the probability of observing of a given number of events for the selected period of…
We demonstrate that the correlations observed in conditioned multiplier distributions of the energy dissipation in fully developed turbulence can be understood as an unavoidable artefact of the observation procedure. Taking the latter into…
We discuss a relativistic diffusion in the proper time in an approach of Schay and Dudley. We derive (Langevin) stochastic differential equations in various coordinates.We show that in some coordinates the stochastic differential equations…
We derive functional equations for distributions of six classical statistics (ascents, descents, left-to-right maxima, right-to-left maxima, left-to-right minima, and right-to-left minima) on separable and irreducible separable…
Recently, Ghashghaie et al. have shown that some statistical aspects of fully developed turbulence and exchange rate fluctuations exhibit striking similarities (Nature 381, 767 (1996)). The authors then suggested that the two problems might…
Making use of a recursive approach, derivative dispersion relations are generalized for an arbitrary number of subtractions. The results for both cross even and odd amplitudes are theoretically consistent at sufficiently high energies and…
In this paper, we study a distribution of labeled particles on a continuous ring. It arises in three different ways, all related to the multi-type TASEP on a ring. We prove formulas for the probability density function for some permutations…
In [G. Garcia-Calderon, J. L. Mateos, and M. Moshinsky, Phys. Rev. Lett. 74, 337 (1995)], the time evolution of the quantum decay of a state initially located within an interaction region of finite range was investigated. In particular, it…
It is demonstrated that the "generalized fluctuation-dissipation theorem" [Physica A 106, 443 (1981)] covers the later suggested "fluctuation theorems" and related statistical equalities.
A more detailed derivation of the Heisenberg uncertainty principle from the certainty principle is given.
In this paper, we study Ruelle's probability cascades in the framework of time-inhomogeneous fragmentation processes. We describe Ruelle's cascades mechanism exhibiting a family of measures $(\nu_t,t\in [0,1[)$ that characterizes its…
Master equations are common descriptions of mesoscopic systems. Analytical solutions to these equations can rarely be obtained. We here derive an analytical approximation of the time-dependent probability distribution of the master equation…
We consider an abstract space of measurable linear cocycles and we assume the availability in this space of some appropriate uniform large deviation type estimates. Under these hypotheses we establish the continuity of the Oseledets…
This paper replies the comment by E. Kapuscik [Am. J. Phys. 77, 754 (2009)]
A cascade model is described based on multiplier distributions determined from 3D direct numerical simulations (DNS) of turbulent particle laden flows, which include two-way coupling between the phases at global mass loadings equal to…
The paper deals with a generalisation of uniform distribution. The analogues of Weyl's criterion are derived.
As an enhanced version of existing results on Kac's propagation of chaos, which describes the convergence of mean-field particle systems to a system of independent McKean-Vlasov particles as the number of particles tends to infinity, we…
In this note, we review some of the recent developments in the well-posedness theory of nonlinear dispersive partial differential equations with random initial data.