We study the long time behaviour of a nonlinear oscillator subject to a random multiplicative noise with a spectral density (or power-spectrum) that decays as a power law at high frequencies. When the dissipation is negligible, physical observables, such as the amplitude, the velocity and the...

The Euler - Maruyama and Milstein methods are applied to approximate the solution of linearly Langevin equation with multiplicative noise. The exact solution is obtained by applying the Ito's lemma. It is worth mentioning that not always the discretization used to find the solutions of SDEs...

The dimensional free Harnack inequality is established for a class of semilinear stochastic partial differential equations in the Hilbert space with multiplicative noise by perturbing the linear term of the equation by a suitable linear operator.

This paper describes a design for a least mean square error estimator in discrete time systems where the components of the state vector, in measurement equation, are corrupted by different multiplicative noises in addition to observation noise. We show how known results can be considered a...

The subject of the present paper is a simplified model for a symmetric bistable system with memory or delay, the reference model, which in the presence of noise exhibits a phenomenon similar to what is known as stochastic resonance. The reference model is given by a one dimensional parametrized...

Thermal pulsations in a transition from a nucleate to a film regime of water boiling on a wire heater with a periodic Joule heat release have been studied experimentally. At frequencies of the periodic action smaller than 0.1 Hz the intermittency of the nucleate and film boiling regimes was...

The model of a stochastic oscillator subject to additive random force, which includes the Brownian motion, is widely used for analysis of different phenomena in physics, chemistry, biology, economics and social science. As a rule, by the appropriate choice of units one assumes that the...

Power spectrum densities for the number of tick quotes per minute (market activity) on three currency markets (USD/JPY, EUR/USD, and JPY/EUR) are analyzed for periods from January 2000 to December 2000. We find some peaks on the power spectrum densities at a few minutes. We develop the...

By using the linear approximation method, the laser intensity power spectrum and signal-to-noise ratio (SNR) are calculated for a gain-noise model of a single-mode laser driven by colored cross-correlated pump noise and quantum noise, each of which is colored. We found that stochastic...