Related papers: Generalised cascades
Discrete multiplicative turbulent cascades are described using a formalism involving infinitely divisible random measures. This permits to consider the continuous limit of a cascade developed on a continuum of scales, and to provide the…
A q-generalization of the product densities in stochastic point processes is developed. The properties of these functions are studied and a q-generalization of the usual $C^r_s$ coefficients is obtained. This for fixed q-number of particles…
This paper is on developing stochastic analysis simultaneously under a general family of probability measures that are not dominated by a single probability measure. The interest in this question originates from the probabilistic…
Multiplicative cascades, under weak or strong disorder, refer to sequences of positive random measures $\mu_{n,\beta}, n = 1,2,\dots$, parameterized by a positive disorder parameter $\beta$, and defined on the Borel $\sigma$-field…
This announcement describes a probabilistic approach to cascades which, in addition to providing an entirely probabilistic proof of the Kahane-Peyri\`ere theorem for independent cascades, readily applies to general dependent cascades.…
A multiplicative cascade can be thought of as a randomization of a measure on the boundary of a tree, constructed from an iid collection of random variables attached to the tree vertices. Given an initial measure with certain regularity…
In this manuscript we introduce a generalisation of the log-Normal distribution that is inspired by a modification of the Kaypten multiplicative process using the $q$-product of Borges [Physica A \textbf{340}, 95 (2004)]. Depending on the…
In the present paper we generate binary pseudorandom sequences using generalized polynomials. A generalized polynomial is a function in whose description we not only allow addition and product (as it is the case in usual polynomials) but…
Markovian properties of a discrete random multiplicative cascade model of log-normal type are discussed. After taking small-scale resummation and breaking of the ultrametric hierarchy into account, qualitative agreement with Kramers-Moyal…
Multiplicative cascades have been introduced in turbulence to generate random or deterministic fields having intermittent values and long-range power-law correlations. Generally this is done using discrete construction rules leading to…
Mandelbrot multiplicative cascades provide a construction of a dynamical system on a set of probability measures defined by inequalities on moments. To be more specific, beyond the first iteration, the trajectories take values in the set of…
We study different fractional extensions of the Poisson process and generalized counting processes by introducing time-change represented by the inverse to the sums of stable and tempered stable subordinators. We state the governing…
I present here some results on the statistical behaviour of large random matrices in an ensemble where the probability distribution is not a function of the eigenvalues only. The perturbative expansion can be cast in a closed form and the…
It is shown that a normalisable probability density can be defined for the entire complex plane in the modified de Broglie-Bohm quantum mechanics, which gives complex quantum trajectories. This work is in continuation of a previous one that…
Generalised two-dimensional (2D) fluid dynamics is characterised by a relationship between a scalar field $q$, called generalised vorticity, and the stream function $\psi$, namely $q = (-\nabla^2)^\frac{\alpha}{2} \psi$. We study the…
Generalized likelihoods are commonly used to obtain consistent estimators with attractive computational and robustness properties. Formally, any generalized likelihood can be used to define a generalized posterior distribution, but an…
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…
This paper introduces and studies a new class of nonparametric prior distributions. Random probability distribution functions are constructed via normalization of random measures driven by increasing additive processes. In particular, we…
In this work we derive an inversion formula for the Laplace transform of a density observed on a curve in the complex domain, which generalizes the well known Post-Widder formula. We establish convergence of our inversion method and derive…
The article is devoted to a new type of measures which are hypercomplex generalizations of Gaussian-type measures. The considered such measures are related with solutions of high order hyperbolic PDEs and related Markov processes. Their…