相关论文: Long and Short Memory in Economics: Fractional-Ord…

In this paper we give simple sufficient conditions for linear type processes with short memory that imply the invariance principle. Various examples including projective criterion are considered as applications. In particular, we treat the…

For a real sequence of length of m = nl, we may deduce its congruence derivative sequence with length of l. The discrete Fourier transform of original sequence can be calculated by the discrete Fourier transform of the congruence derivative…

Our work explore the time evolution of entanglement, local quantum uncertainty, and correlated coherence, within a system modeled by two double quantum dots. The dynamics is represented using a time-fractional Schr\"odinger equation, which…

Over the last decade, it has been demonstrated that many systems in science and engineering can be modeled more accurately by fractional-order than integer-order derivatives, and many methods are developed to solve the problem of fractional…

The main objective of this article is to present $\nu$-fractional derivative $\mu$-differentiable functions by considering 4-parameters extended Mittag-Leffler function (MLF). We investigate that the new $\nu$-fractional derivative…

We consider the evolution of correlation functions in a non-Markov version of the contact model in the continuum. The memory effects are introduced by assuming the fractional evolution equation for the statistical dynamics. This leads to a…

Linear Logic refines Intuitionnistic Logic by taking into account the resources used during the proof and program computation. In the past decades, it has been extended to various frameworks. The most famous are indexed linear logics which…

We discuss how to construct reliably well "a lattice and an integer time" version of a super-diffusive continuous-space and -time fractional Brownian motion (fBm) -- an experimentally-relevant non-Markovian Gaussian stochastic process with…

The aim of this paper is to present a simple stochastic model that accounts for the effects of a long-memory in volatility on option pricing. The starting point is the stochastic Black-Scholes equation involving volatility with long-range…

In this article, we provide different representations for a time-fractional birth and death process $N_{\alpha}(t)$, whose transition probabilities are governed by a time-fractional system of differential equations. More specifically, we…

The systematic development of Coarse-Grained (CG) models via the Mori-Zwanzig projector operator formalism requires the explicit description of several terms, including a deterministic drift term, a dissipative memory term and a random…

This paper is dedicated to clarifying and introducing the correct application of Melnikov method in fractional dynamics. Attention to the complex dynamics of hyperbolic orbits and to fractional calculus can be, respectively, traced back to…

In this paper, given a certain regularity of a function $v$, we derive an explicit formula relating the order $\nu_0\in(0,1)$ of the leading fractional derivative in a fractional differential operator $\mathbf{D_t}$ with the variable…

The FARIMA models, which have long-range-dependence (LRD), are widely used in many areas. Through deriving a precise characterisation of the spectrum, autocovariance function, and variance time function, we show that this family is very…

Forecasting time series data is an important subject in economics, business, and finance. Traditionally, there are several techniques to effectively forecast the next lag of time series data such as univariate Autoregressive (AR),…

Many real time-series exhibit behavior adequate to long range dependent data. Additionally very often these time-series have constant time periods and also have characteristics similar to Gaussian processes although they are not Gaussian.…

Memorization of the relation between entities in a dataset can lead to privacy issues when using a trained model for question answering. We introduce Relational Memorization (RM) to understand, quantify and control this phenomenon. While…

This paper presents a data-integrated framework for learning the dynamics of fractional-order nonlinear systems in both discrete-time and continuous-time settings. The proposed framework consists of two main steps. In the first step,…

We consider a utility maximization problem in a broad class of markets. Apart from traditional semimartingale markets, our class of markets includes processes with long memory, fractional Brownian motion and related processes, and, in…

The normalization condition, average values and reduced distribution functions can be generalized by fractional integrals. The interpretation of the fractional analog of phase space as a space with noninteger dimension is discussed. A…