In this work, we develop an analog circuit to generate a stochastic signal with stationary distribution exhibiting a tunable power-law tail. The proposed circuit design is a variant of a recently introduced one based on a differential equation with both multiplicative and additive noises. Here,...

The first two moments of an underdamped harmonic oscillator were found for additive and multiplicative noises. A detailed analysis is performed of the case of a random damping which supplements the case of a random frequency which has received the most study. In both cases the second moments are...

Parameter-induced aperiodic stochastic resonance (SR) in the presence of multiplicative and additive noise is investigated in detail. Using theoretical and numerical analysis, we evaluate the dynamical probability density, by which the bit error rate is defined as a quantity to optimize in the...

We study a model of a nonlinear oscillator with a random frequency and derive the asymptotic behavior of the probability distribution function when the noise is white. In the small damping limit, we show that the physical observables grow algebraically with time before the dissipative time scale...

We introduce a simple generalization of rational bubble models which removes the fundamental problem discovered by Lux and Sornette (J. Money, Credit and Banking, preprint at http://xxx.lanl.gov/abs/cond-mat/9910141) that the distribution of returns is a power law with exponent <1, in contradiction with empirical data. The idea is that the price fluctuations associated with bubbles must on average grow with the mean market return r. When r is larger than the discount rate rδ, the distribution of returns of the observable price, sum of the bubble component and of the fundamental price, exhibits an intermediate tail with an exponent which can be larger than 1. This regime r>rδ corresponds...</1,>

A new model of a financial market is introduced extending the multidimensional Black-Scholes model to the case where several assets can interact with each other even in the absence of noise. Sufficient conditions for the existence of the equivalent martingale measure, absence of arbitrage and...