Related papers: Analysis of data sets of stochastic systems
The functional method to derive the fractional Fokker-Planck equation for probability distribution from the Langevin equation with Levy stable noise is proposed. For the Cauchy stable noise we obtain the exact stationary probability density…
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…
A random multiplicative process with additive noise is described by a Langevin equation. We show that the fluctuation-dissipation relation is satisfied in the Langevin model, if the noise strength is not so strong.
Stochastic averaging allows for the reduction of the dimension and complexity of stochastic dynamical systems with multiple time scales, replacing fast variables with statistically equivalent stochastic processes in order to analyze…
The measured time series from complex systems are renowned for their intricate stochastic behavior, characterized by random fluctuations stemming from external influences and nonlinear interactions. These fluctuations take diverse forms,…
A wide class of nonlinear Langevin equations with drift and diffusion coefficients separable in time and space driven by the Gaussian white noise is analyzed in terms of a generalized n-moment. We show the system may present ergodic…
In this paper, a non-autonomous stochastic logistic system is considered. An interesting result on the effect of stochastically perturbation for the dynamic behavior are obtained. That is, under certain conditions the stochastic system have…
Straightforward method for the derivation of linearized version of stochastic stability analysis of the nonlinear differential equations is presented. Methods for the study of large time behavior of the moments are exposed. These general…
Dimensional reduction techniques have long been used to visualize the structure and geometry of high dimensional data. However, most widely used techniques are difficult to interpret due to nonlinearities and opaque optimization processes.…
A theory of systems with long-range correlations based on the consideration of binary N-step Markov chains is developed. In the model, the conditional probability that the i-th symbol in the chain equals zero (or unity) is a linear function…
We develop further ideas on how to construct low-dimensional models of stochastic dynamical systems. The aim is to derive a consistent and accurate model from the originally high-dimensional system. This is done with the support of centre…
This work is concerned with existence of weak solutions to discon- tinuous stochastic differential equations driven by multiplicative Gaus- sian noise and sliding mode control dynamics generated by stochastic differential equations with…
Pervasive across diverse domains, stochastic systems exhibit fluctuations in processes ranging from molecular dynamics to climate phenomena. The Langevin equation has served as a common mathematical model for studying such systems, enabling…
When the complete understanding of a complex system is not available, as, e.g., for systems considered in the real-world, we need a top-down approach to complexity. In this approach one may start with the desire to understand general…
How to distinguish and quantify deterministic and random influences on the statistics of turbulence data in meteorology cases is discussed from first principles. Liquid water path (LWP) changes in clouds, as retrieved from radio signals,…
We use an effective Markovian description to study the long-time behaviour of a nonlinear second order Langevin equation with Gaussian noise. When dissipation is neglected, the energy of the system grows as with time a power-law with an…
Motivated by stochastic models of climate phenomena, the steady-state of a linear stochastic model with additive Gaussian white noise is studied. Fluctuation theorems for nonequilibrium steady-states provide a constraint on the character of…
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…
Many complex systems operating far from the equilibrium exhibit stochastic dynamics that can be described by a Langevin equation. Inferring Langevin equations from data can reveal how transient dynamics of such systems give rise to their…
Systems are studied in which transport is possible due to large extension with open boundaries in certain directions but the particles responsible for transport can disappear from it by leaving it in other directions, by chemical reaction…