Bernardo Spagnolo

Noise-enhanced stability of periodically driven metastable states.

We study the effect of noise-enhanced stability of periodically driven metastable states in a system described by piecewise linear potential. We find that the growing of the average escape time with the intensity of the noise is depending on the initial condition of the system. We analytically obtain the condition for the noise enhanced stability effect and verify it by numerical simulations.

Noise-enhanced stability in fluctuating metastable states

We derive general equations for the nonlinear relaxation time of Brownian diffusion in randomly switching potential with a sink. For piece-wise linear dichotomously fluctuating potential with metastable state, we obtain the exact average lifetime as a function of the potential parameters and the noise intensity. Our result is valid for arbitrary white noise intensity and for arbitrary fluctuation rate of the potential. We find noise enhanced stability phenomenon in the system investigated: The average lifetime of the metastable state is greater than the time obtained in the absence of additive white noise. We obtain the parameter region of the fluctuating potential where the effect can be observed. The system investigated also exhibits a maximum of the lifetime as a function of the fluctuation rate of the potential.

Stochastic resonance and noise delayed extinction in a model of two competing species

We study the role of the noise in the dynamics of two competing species. We consider generalized Lotka–Volterra equations in the presence of a multiplicative noise, which models the interaction between the species and the environment. The interaction parameter between the species is a random process which obeys a stochastic differential equation with a generalized bistable potential in the presence of a periodic driving term, which accounts for the environment temperature variation. We find noise-induced periodic oscillations of the species concentrations and stochastic resonance phenomenon. We find also a nonmonotonic behavior of the mean extinction time of one of the two competing species as a function of the additive noise intensity.

Signatures of noise-enhanced stability in metastable states.

The lifetime of a metastable state in the transient dynamics of an overdamped Brownian particle is analyzed, both in terms of the mean first passage time and by means of the mean growth rate coefficient. Both quantities feature nonmonotonic behaviors as a function of the noise intensity, and are independent signatures of the noise enhanced stability effect. They can therefore be alternatively used to evaluate and estimate the presence of this phenomenon, which characterizes metastability in nonlinear physical systems.

Mean Escape Time in a System with Stochastic Volatility

We study the mean escape time in a market model with stochastic volatility. The process followed by the volatility is the Cox, Ingersoll, and Ross process which is widely used to model stock price fluctuations. The market model can be considered as a generalization of the Heston model, where the geometric Brownian motion is replaced by a random walk in the presence of a cubic nonlinearity. We investigate the statistical properties of the escape time of the returns, from a given interval, as a function of the three parameters of the model. We find that the noise can have a stabilizing effect on the system, as long as the global noise is not too high with respect to the effective potential barrier experienced by a fictitious Brownian particle. We compare the probability density function of the return escape times of the model with those obtained from real market data. We find that they fit very well.

Experimental investigation of resonant activation

We experimentally investigate the escape from a metastable state over a fluctuating barrier of a physical system. The system is switching between two states under electronic control of a dichotomous noise. We measure the escape time and its probability density function as a function of the correlation rate of the dichotomous noise in a frequency interval spanning more than four frequency decades. We observe resonant activation, namely a minimum of the average escape time as a function of the correlation rate. We detect two regimes in the study of the shape of the escape time probability distribution: (i) a regime of exponential and (ii) a regime of nonexponential probability distribution.

Stability measures in metastable states with Gaussian colored noise

We present a study of the escape time from a metastable state of an overdamped Brownian particle in the presence of colored noise generated by Ornstein-Uhlenbeck process. We analyze the role of the correlation time on the enhancement of the mean first passage time through a potential barrier and on the behavior of the mean growth rate coefficient as a function of the noise intensity. We observe the noise-enhanced stability effect for all the initial unstable states used and for all values of the correlation time tau(c) investigated. We can distinguish two dynamical regimes characterized by weak and strong correlated noises, depending on the value of tau(c) with respect to the relaxation time of the system.

Co-occurrence of resonant activation and noise-enhanced stability in a model of cancer growth in the presence of immune response

We investigate a stochastic version of a simple enzymatic reaction which follows the generic Michaelis-Menten kinetics. At sufficiently high concentrations of reacting species, that represent here populations of cells involved in cancerous proliferation and cytotoxic response of the immune system, the overall kinetics can be approximated by a one-dimensional overdamped Langevin equation. The modulating activity of the immune response is here modeled as a dichotomous random process of the relative rate of neoplastic cell destruction. We discuss physical aspects of environmental noises acting in such a system, pointing out the possibility of coexistence of dynamical regimes where noise-enhanced stability and resonant activation phenomena can be observed together. We explain the underlying mechanisms by analyzing the behavior of the variance of first passage times as a function of the noise intensity.

Hitting time distributions in financial markets

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 composed by daily price of 1071 stocks trade for the 12-year period 1987–1998, the second one is composed by high frequency data for 100 stocks for the 4-year period 1995–1998. We compare the probability distribution obtained by our empirical analysis with those obtained from different models for stock market evolution. Specifically by focusing on the statistical properties of the hitting times to reach a barrier or a given threshold, we compare the probability density function (PDF) of three models, namely the geometric Brownian motion, the GARCH model and the Heston model with that obtained from real market data. We will present also some results of a generalized Heston model.

Stochastic resonance in magnetic systems described by Preisach hysteresis model

We present a numerical study of stochastic resonance in magnetic systems described by Preisach hysteresis model. It is shown that stochastic resonance occurs in these systems. Specifically, the signal-to-noise ratio (SNR) and the signal amplification (SA) present a maximum as a function of noise intensity. We also found that the hysteresis loops, dynamically described by the system, are strongly modified near the maxima of SNR and of SA.