Related papers: Modelling High-frequency Economic Time Series
We study the stochastic motion of particles driven by long-range correlated fractional Gaussian noise in a superharmonic external potential of the form $U(x)\propto x^{2n}$ ($n\in\mathbb{N}$). When the noise is considered to be external,…
We provide a Lyapunov convergence analysis for time-inhomogeneous variable coefficient stochastic differential equations (SDEs). Three typical examples include overdamped, irreversible drift, and underdamped Langevin dynamics. We first…
Non-Markovian models have great expressive power, at the cost of complex analysis of the stochastic process. The method of Stochastic State Classes (SSCs) derives closed-form analytical expressions for the joint Probability Density…
This study explores contagion in the Chinese stock market using Hawkes processes to analyze autocorrelation and cross-correlation in multivariate time series data. We examine whether market indices exhibit trending behavior and whether…
This work is an attempt to transfer to biology the methods developed in physics for formulating and solving the kinetic equations in which the kernel of the integral operator in spatial coordinates is slowly decreasing with increasing…
The probability density function (PDF) of flux $R$ is computed in systems with logarithmic non-linearity using a model non-linear dynamical equation. The PDF tails of the first moment flux are analytically predicted to be power law. These…
A theory which describes the share price evolution at financial markets as a continuous-time random walk has been generalized in order to take into account the dependence of waiting times t on price returns x. A joint probability density…
Spatio-temporally extended nonlinear systems often exhibit a remarkable complexity in space and time. In many cases, extensive datasets of such systems are difficult to obtain, yet needed for a range of applications. Here, we present a…
A method providing optimal estimate of probability density functions (PDFs) from time series is proposed. It allows almost arbitrary resolution PDFs when applied to either, sampled analytic functions or digitized data from experiments. When…
We present a new time-dependent Density Functional approach to study the relaxational dynamics of an assembly of interacting particles subject to thermal noise. Starting from the Langevin stochastic equations of motion for the velocities of…
In molecular dynamics, statistics of transitions, such as the mean transition time, are macroscopic observables which provide important dynamical information on the underlying microscopic stochastic process. A direct estimation using…
In [20], the authors addressed the question of the averaging of a slow-fast Piecewise Deterministic Markov Process (PDMP) in infinite dimension. In the present paper, we carry on and complete this work by the mathematical analysis of the…
A microscopic model is established for financial Brownian motion from the direct observation of the dynamics of high-frequency traders (HFTs) in a foreign exchange market. Furthermore, a theoretical framework parallel to molecular kinetic…
Many systems in nature and laboratories are far from equilibrium and exhibit significant fluctuations, invalidating the key assumptions of small fluctuations and short memory time in or near equilibrium. A full knowledge of Probability…
Supersonic turbulence occurs in many environments, particularly in astrophysics. In the crucial case of isothermal turbulence, the probability density function (PDF) of the logarithmic density, $s$, is well measured, but a theoretical…
Complex systems display anomalous diffusion, whose signature is a space/time scaling $x\sim t^\delta$ with $\delta \ne 1/2$ in the Probability Density Function (PDF). Anomalous diffusion can emerge jointly with both Gaussian, e.g.,…
The probability distributions, as well as the mean values of stochastic currents and fluxes, associated with a driven Langevin process, provide a good and topologically protected measure of how far a stochastic system is driven out of…
Recovering a stochastic process from noisy ensembles of single particle trajectories (SPTs) is resolved here using the Langevin equation as a model. The massive redundancy contained in SPTs data allows recovering local parameters of the…
We consider the inverse problem of reconstructing the posterior measure over the trajec- tories of a diffusion process from discrete time observations and continuous time constraints. We cast the problem in a Bayesian framework and derive…
If two probability density functions (PDFs) have values for their first $n$ moments which are quite close to each other (upper bounds of their differences are known), can it be expected that the PDFs themselves are very similar? Shown below…