Related papers: Fractional contact model in the continuum
In this paper, we revisit the notion of partial copula, originally introduced to test conditional independence, highlighting its capability to represent the dependence between two random variables after removing their dependence with a…
Anomalous relaxation and diffusion processes have been widely characterized by fractional derivative models, where the definition of the fractional-order derivative remains a historical debate due to the singular memory kernel that…
A conservative Feller evolution on continuous bounded functions is constructed from a weakly continuous, time-inhomogeneous transition function describing a pure jump process on a locally compact Polish space. The transition function is…
Time-dependent conformal maps are used to model a class of growth phenomena limited by coupled non-Laplacian transport processes, such as nonlinear diffusion, advection, and electro-migration. Both continuous and stochastic dynamics are…
Integer-order differential operators were originally used to describe local and isotropic effects, in both space and time. However, in fields like biology, the modelling of complex phenomena with spatial heterogeneity necessitates more…
Viscoelasticity and related phenomena are of great importance in the study of mechanical properties of material especially, biological materials. Certain materials show some complex effects in mechanical tests, which cannot be described by…
Fractional order differential and difference equations are used to model systems with memory. Variable order fractional equations are proposed to model systems where the memory changes in time. We investigate stability conditions for linear…
Designing effective neural networks requires tuning architectural elements. This study integrates fractional calculus into neural networks by introducing fractional order derivatives (FDO) as tunable parameters in activation functions,…
A space fractional diffusion-like equation is introduced, which embodies the nonlocality in time, represented by the memory kernel and the non-locality in space. A specific example of the nonlocal term is considered in combination with…
In this work we propose a new class of long-memory models with time-varying fractional parameter. In particular, the dynamics of the long-memory coefficient, $d$, is specified through a stochastic recurrence equation driven by the score of…
An individual-based model of an infinite system of point particles in $\mathbb{R}^d$ is proposed and studied. In this model, each particle at random produces a finite number of new particles and disappears afterwards. The phase space for…
Fractional moments have been investigated by many authors to represent the density of univariate and bivariate random variables in different contexts. Fractional moments are indeed important when the density of the random variable has…
Phylogenetics uses alignments of molecular sequence data to learn about evolutionary trees relating species. Along branches, sequence evolution is modelled using a continuous-time Markov process characterised by an instantaneous rate…
The developing of (non-Markovian) memory effects strongly depends on the underlying system-environment dynamics. Here we study this problem in multipartite arrangements where all subsystems are coupled to each other by non-diagonal…
The idea of fractional derivatives has a long history that dates back centuries. Apart from their intriguing mathematical properties, fractional derivatives have been studied widely in physics, for example in quantum mechanics and generally…
The short-time dynamics of correlated systems is strongly influenced by initial correlations giving rise to an additional collision integral in the non-Markovian kinetic equation. Exact cancellation of the two integrals is found if the…
Many empirical studies estimate causal effects in environments where economic units interact through spatial or network connections. In such settings, outcomes are jointly determined, and treatment induced shocks propagate across…
This article proposes methods to model nonstationary temporal graph processes. This corresponds to modelling the observation of edge variables (relationships between objects) indicating interactions between pairs of nodes (or objects)…
The records statistics in stationary and non-stationary fractal time series is studied extensively. By calculating various concepts in record dynamics, we find some interesting results. In stationary fractional Gaussian noises, we observe a…
We present Fractional Diffusion Bridge Models (FDBM), a novel generative diffusion bridge framework driven by an approximation of the rich and non-Markovian fractional Brownian motion (fBM). Real stochastic processes exhibit a degree of…