Related papers: Multifractal processes: Definition, properties and…
Under the formalism of annealed averaging of the partition function, two types of random multifractal measures with their probability of multipliers satisfying power distribution and triangular distribution are investigated mathematically.…
Stochastic growth processes give rise to diverse intricate structures everywhere and across all scales in nature. Despite the seemingly unrelated complex phenomena at their origin, the Laplacian growth theory has succeeded in unifying their…
The Random Parameters model was proposed to explain the structure of the covariance matrix in problems where most, but not all, of the eigenvalues of the covariance matrix can be explained by Random Matrix Theory. In this article, we…
We investigate the properties of multifractal products of geometric Gaussian processes with possible long-range dependence and geometric Ornstein-Uhlenbeck processes driven by L\'{e}vy motion and their finite and infinite superpositions. We…
We suggest to investigate certain non-standard (pseudo-)differential operators in order to construct and to study multi-parameter processes. Our approach will include "classical" multi-parameter Markov processes but will go eventually far…
We present a general class of spatio-temporal stochastic processes describing the causal evolution of a positive-valued field in space and time. The field construction is based on independently scattered random measures of Levy type whose…
This work defines two classes of processes, that we term {\it tempered fractional multistable motion} and {\it tempered multifractional stable motion}. They are extensions of fractional multistable motion and multifractional stable motion,…
An estimation method is proposed for a wide variety of discrete time stochastic processes that have an intractable likelihood function but are otherwise conveniently specified by an integral transform such as the characteristic function,…
We study a branching-process random iterated function system (RIFS) defined by a recursive replacement of leaves by finite subtrees at strictly smaller contraction scales. This construction yields a tree-valued, infinite-depth random…
We introduce a multistable subordinator, which generalizes the stable subordinator to the case of time-varying stability index. This enables us to define a multifractional Poisson process. We study properties of these processes and…
This paper revisits the definition of linear time-invariant (LTI) stochastic process within a behavioral systems framework. Building on [Willems, 2013], we derive a canonical representation of an LTI stochastic process and a physically…
Towards the end of the last century, B. Mandelbrot saw the importance, revealed the beauty, and robustly promoted (multi-)fractals. Multiplicative cascades are closely related and provide simple models for the study of turbulence and chaos.…
We construct a modified continuous-state branching process whose Malthusian parameter is replaced by another when passing below a certain level. The construction is obtained via a Lamperti-like transform applied to a refracted L\'evy…
Multifractal scaling has been extensively studied for real-valued stochastic processes, but a systematic integer-valued analogue has remained largely unexplored. In this work, we introduce a multifractal framework for integer-valued…
Recently the statistical characterizations of financial markets based on physics concepts and methods attract considerable attentions. We used two possible procedures of analyzing multifractal properties of a time series. The first one uses…
We analyze invariant measures of two coupled piecewise linear and everywhere expanding maps on the synchronization manifold. We observe that though the individual maps have simple and smooth functions as their stationary densities, they…
The n-point statistics of singularity strength variables for multiplicative branching processes is calculated from an analytic expression of the corresponding multivariate generating function. The key ingredient is a branching generating…
In this course, we propose an elementary and self-contained introduction to canonical Mandelbrot random cascades. The multiplicative construction is explained and the necessary and sufficient condition of non-degeneracy is proved. Then, we…
We introduce a local multifractal formalism adapted to functions, measures or distributions which display multifractal characteristics that can change with time, or location. We develop this formalism in a general framework and we work out…
Data series generated by complex systems exhibit fluctuations on many time scales and/or broad distributions of the values. In both equilibrium and non-equilibrium situations, the natural fluctuations are often found to follow a scaling…