相关论文: Modelling High-frequency Economic Time Series
Dispersion of a passive scalar from concentrated sources in fully developed turbulent channel flow is studied with the probability density function (PDF) method. The joint PDF of velocity, turbulent frequency and scalar concentration is…
Recent rapid advances in single particle tracking and supercomputing techniques resulted in an unprecedented abundance of diffusion data exhibiting complex behaviours, such the presence of power law tails of the msd and memory functions,…
Functionals of particles' paths have diverse applications in physics, mathematics, hydrology, economics, and other fields. Under the framework of continuous time random walk (CTRW), the governing equations for the probability density…
A step by step procedure to derive analytically the exact dynamical evolution equations of the probability density functions (PDF) of well known kinetic wealth exchange economic models is shown. This technique gives a dynamical insight into…
We study the dynamics of Brownian particles in a heterogeneous one-dimensional medium with a spatially-dependent diffusion coefficient of the form $D(x)\sim |x|^c$, at constant temperature. The particle's probability distribution function…
In probability density function (PDF) methods a transport equation is solved numerically to compute the time and space dependent probability distribution of several flow variables in a turbulent flow. The joint PDF of the velocity…
We study the extremal properties of a stochastic process $x_t$ defined by a Langevin equation $\dot{x}_t=\sqrt{2 D_0 V(B_t)}\,\xi_t$, where $\xi_t$ is a Gaussian white noise with zero mean, $D_0$ is a constant scale factor, and $V(B_t)$ is…
We introduce a stochastic equation for the microscopic motion of a tagged particle in the single file model. This equation provides a compact representation of several of the system's properties such as Fluctuation-Dissipation and Linear…
The shape and tails of partial distribution functions (PDF) for a financial signal, i.e. the S&P500 and the turbulent nature of the markets are linked through a model encompassing Tsallis nonextensive statistics and leading to evolution…
We study Langevin dynamics with stochastic diffusivity arising from fluctuations of the surrounding medium. The diffusivity is modeled as Ornstein-Uhlenbeck process driven by symmetric dichotomous noise, which confines it to a finite…
The diffusion of colloids inside an active system-e.g. within a living cell or the dynamics of active particles itself (e.g. self-propelled particles) can be modeled through overdamped Langevin equation which contains an additional noise…
We study a Langevin equation describing the stochastic motion of a particle in one dimension with coordinate $x$, which is simultaneously exposed to a space-dependent friction coefficient $\gamma(x)$, a confining potential $U(x)$ and…
We analyze the hitting time distributions of stock price returns in different time windows, characterized by different levels of noise present in the market. The study has been performed on two sets of data from US markets. The first one is…
Random processes play a crucial role in scientific research, often characterized by distribution functions or probability density functions (PDFs). These PDFs serve as essential approximations of the actual and frequently undisclosed…
We show the relation between processes which are modeled by a Langevin equation with multiplicative noise and infinite ergodic theory. We concentrate on a spatially dependent diffusion coefficient that behaves as ${D(x)}\sim…
Price movements of stock market are not totally random. In fact, what drives the financial market and what pattern financial time series follows have long been the interest that attracts economists, mathematicians and most recently computer…
We present a time-dependent Langevin description of dynamics of stock prices. Based on a simple sliding-window algorithm, the fluctuation of stock prices is discussed in the view of a time-dependent linear restoring force which is the…
Stochastic resetting is a rapidly developing topic in the field of stochastic processes and their applications. It denotes the occasional reset of a diffusing particle to its starting point and effects, inter alia, optimal first-passage…
Mathematical models based on probability density functions (PDF) have been extensively used in hydrology and subsurface flow problems, to describe the uncertainty in porous media properties (e.g., permeability modelled as random field).…
We review the latest advances in the analytical modelling of single file diffusion. We focus first on the derivation of the fractional Langevin equation that describes the motion of a tagged file particle. We then propose an alternative…