Related papers: Integer-valued multifractal processes
We consider the hierarchic tree Random Energy Model with continuous branching and calculate the moments of the corresponding partition function. We establish the multifractal properties of those moments. We derive formulas for the normal…
We introduce a new class of processes for the evaluation of multivariate equity derivatives. The proposed setting is well suited for the application of the standard copula function theory to processes, rather than variables, and easily…
We formulate the statistics of the discrete multicomponent fragmentation event using a methodology borrowed from statistical mechanics. We generate the ensemble of all feasible distributions that can be formed when a single integer…
Stochastic processes play a fundamental role in physics, mathematics, engineering and finance. One potential application of quantum computation is to better approximate properties of stochastic processes. For example, quantum algorithms for…
Gaussian processes (GPs) are frequently used in machine learning and statistics to construct powerful models. However, when employing GPs in practice, important considerations must be made, regarding the high computational burden,…
We apply general moment identities for Poisson stochastic integrals with random integrands to the computation of the moments of Markovian growth-collapse processes. This extends existing formulas for mean and variance available in the…
We introduce a general notion of fractional (noninteger) derivative for functions defined on arbitrary time scales. The basic tools for the time-scale fractional calculus (fractional differentiation and fractional integration) are then…
Many problems require to approximate an expected value by some kind of Monte Carlo (MC) sampling, e.g. molecular dynamics (MD) or simulation of stochastic reaction models (also termed kinetic Monte Carlo (kMC)). Often, we are furthermore…
A wide range of problems in computational science and engineering require estimation of sparse eigenvectors for high dimensional systems. Here, we propose two variants of the Truncated Orthogonal Iteration to compute multiple leading…
This article introduces a functional method for lower-dimensional smooth representations in terms of time-varying dissimilarities. The method incorporates dissimilarity representation in multidimensional scaling and smoothness approach of…
The Ornstein-Uhlenbeck process can be seen as a paradigm of a finite-variance and statistically stationary rough random walk. Furthermore, it is defined as the unique solution of a Markovian stochastic dynamics and shares the same local…
We present a highly scalable algorithm for multiplying sparse multivariate polynomials represented in a distributed format. This algo- rithm targets not only the shared memory multicore computers, but also computers clusters or specialized…
These notes survey some aspects of discrete-time chaotic calculus and its applications, based on the chaos representation property for i.i.d. sequences of random variables. The topics covered include the Clark formula and predictable…
We propose a nonparametric factorization approach for sparsely observed tensors. The sparsity does not mean zero-valued entries are massive or dominated. Rather, it implies the observed entries are very few, and even fewer with the growth…
Multifractal analysis has become a powerful signal processing tool that characterizes signals or images via the fluctuations of their pointwise regularity, quantified theoretically by the so-called multifractal spectrum. The practical…
We present a simple stochastic algorithm for generating multiplicative processes with multiscaling both in space and in time. With this algorithm we are able to reproduce a synthetic signal with the same space and time correlation as the…
It is known that backward iterations of independent copies of a contractive random Lipschitz function converge almost surely under mild assumptions. By a sieving (or thinning) procedure based on adding to the functions time and space…
We use a discrete multiscale analysis to study the asymptotic integrability of differential-difference equations. In particular, we show that multiscale perturbation techniques provide an analytic tool to derive necessary integrability…
Collisionless suspensions of inertial particles (finite-size impurities) are studied in 2D and 3D spatially smooth flows. Tools borrowed from the study of random dynamical systems are used to identify and to characterise in full generality…
We develop a multifractal random tilling that fills the square. The multifractal is formed by an arrangement of rectangular blocks of different sizes, areas and number of neighbors. The overall feature of the tilling is an heterogeneous and…