Logarithmic gaps have been used in order to find a periodic component of the sequence of prime numbers, hidden by a random noise stochastic or chaotic . It is shown that multiplicative nature of the noise is the main reason for the successful application of the logarithmic gaps transforming the multiplicative noise into an additive one. A relation of this phenomenon to spontaneous neuron activi...

We consider attractors for certain types of random dynamical systems. These are skew-product systems whose base transformations preserve an ergodic invariant measure. We discuss definitions of invariant sets, attractors and invariant measures for deterministic and random dynamical systems. Under assumptions that include, for example, iterated function systems, but that exclude stochastic differ...

We present a set of models of the main stylized facts of market price fluctuations. These models comprise dynamical evolution with threshold dynamics and Langevin price equation with multiplicative noise, percolation models to describe the interaction between traders and hierarchical cascade models to unravel the possible correlation accross time scales, including the log-periodic signatures as...

We prove the validity of an averaging principle for a class of systems of slow-fast reaction-diffusion equations with the reaction terms in both equations having polynomial growth, perturbed by a noise of multiplicative type. The models we have in mind are the stochastic Fitzhugh– Nagumo equation arising in neurophysiology and the Ginzburg–Landau equation arising in statistical mechanics.

i.e., there exists a constant C such that SN(θ, u) ≤ CN . We define δ(θ, u) to be the infimum of the δ satisfying H1 for θ and u. About H1, in the case where θ takes its values in U (the set of complex numbers of modulus 1), it is clear that for all sequences θ and u, δ(θ, u) is smaller than or equal to 1 and it is well-known (see [Ka] for example) that it is greater than or equal to 1/2. Few e...

Effects of multiplicative noise on optical bistability in a three-level atomic medium in a ring cavity are investigated experimentally and theoretically. Steady-state intensity distributions as well as switching and dwell times have been measured as functions of noise strength. System response to an external periodic signal is also explored. It is found that the probability for the system to st...

The qualitative properties of local random invariant manifolds for stochastic partial differential equations with quadratic nonlinearities and multiplicative noise is studied by a cut off technique. By a detail estimates on the Perron fixed point equation describing the local random invariant manifold, the structure near a bifurcation is given.

Klein [Klein, A. S. (2006). Separating transducer nonlinearities and multiplicative noise in contrast discrimination. Vision Research, 46, 4279–4293] questions the existence of intrinsic singularities in two-alternative force-choice (2AFC) Signal Detection Theory (SDT) models, suggesting that the singularities found in Katkov et al. [Katkov, M., Tsodyks, M., & Sagi, D. (2006a). Singularities in...

In this paper we study the asymptotic dynamics of the stochastic strongly damped wave equation with multiplicative noise under homogeneous Dirichlet boundary condition. We investigate the existence of a compact random attractor for the random dynamical system associated with the equation.

semilinear stochastic evolution equations with multiplicative l'evy noise are considered‎. ‎the drift term is assumed to be monotone nonlinear and with linear growth‎. ‎unlike other similar works‎, ‎we do not impose coercivity conditions on coefficients‎. ‎we establish the continuous dependence of the mild solution with respect to initial conditions and also on coefficients. ‎as corollaries of ...