A Langevin-type equation for stochastic processes with a periodical correlation function is introduced. A procedure of reconstruction of the equation from time series is proposed and verified on simulated data. The method is applied to geophysical time series–hourly time series of wind speed...

In this paper, we investigate the stochastic spread of epidemics and rumours on networks. We focus on the general stochastic (SIR) epidemic model and a recently proposed rumour model on networks in Nekovee et al. (2007) [3], and on networks with different random structures, taking into account...

We prove that Student’s t-distribution provides one of the better fits to returns of S&P component stocks and the generalized inverse gamma distribution best fits VIX and VXO volatility data. We further prove that stock returns are best fit by the product distribution of the generalized...

We extend Kirman’s model by introducing variable event time scale. The proposed flexible time scale is equivalent to the variable trading activity observed in financial markets. Stochastic version of the extended Kirman’s agent based model is compared to the non-linear stochastic models of...

A new class of stochastic variables, governed by a specific set of rules, is introduced. These rules force them to loose some properties usually assumed for this kind of variables. We demonstrate that stochastic processes driven by these random sources must be described using a probability...

Several mathematical models have been proposed to predict the activation state of a transcription factor (TF) from the expression levels of its target genes. This inference problem is complicated however due to the fact that different genes may be regulated by different activation schemes...

We discuss stochastic modeling of volatility persistence and anti-correlations in electricity spot prices, and for this purpose we present two mean-reverting versions of the multifractal random walk (MRW). In the first model the anti-correlations are modeled in the same way as in an...

Maximum likelihood estimation techniques for multifractal processes are applied to high-frequency data in order to quantify intermittency in the fluctuations of asset prices. From time records as short as one month these methods permit extraction of a meaningful intermittency parameter λ...

The aim of this paper is to explain why Statistical Physics can help understanding two related linguistic questions. The first question is how to model first language acquisition by a child. The second question is how language change proceeds in time.