A model of a system driven by quantum white noise with singular quadratic self–interaction is considered and an exact solution for the evolution operator is found. It is shown that the renormalized square of the squeezed classical white noise is equivalent to the quantum Poisson process. We describe how equations driven by nonlinear functionals of white noise can be derived in nonlinear quantum...

We consider Gaussian, Poissonian, fractional Gaussian and fractional Poissonian white noise spaces, all represented through the corresponding orthogonal basis of the Hilbert space of random variables with finite second moments, given by the Hermite and the Charlier polynomials. There exist unitary mappings between the Gaussian and Poissonian white noise spaces. We investigate the relationship o...

Beneficial effects of noise on higher cognition have recently attracted attention. Hypothesizing an involvement of the mesolimbic dopamine system and its functional interactions with cortical areas, the current study aimed to demonstrate a facilitation of dopamine-dependent attentional and mnemonic functions by externally applying white noise in five behavioral experiments including a total sam...

Although feedback does not increase capacity of an additive white noise Gaussian channel, it enables prediction of the noise for non-white additive Gaussian noise channels and results in an improvement of capacity, but at most by a factor of 2 (Pinsker, Ebert, Pombra, and Cover). Although the capacity of white noise channels cannot be increased by feedback, multiple access white noise channels ...

The reliability of dynamic systems modeled by white noise excited, stochastic, ordinary di erential equations can be computed from deterministic backward Kolmogorov equations. This paper discusses and compares some numerical solution methods for boundary value problems involving backward Kolmogorov equations. The numerical examples concern single degree of freedom oscillators subjected to white...

In electronic measurements, one observes “signals,” which must be distinctly above the “noise.” Noise induced from outside sources may be reduced by shielding and proper “grounding.” Less noise means greater sensitivity with signal/noise as the figure of merit. However, there exist fundamental sources of noise which no clever circuit can avoid. The intrinsic noise is a result of the thermal jit...

Millisecond and binary pulsars are the most stable astronomical standards of frequency. They can be applied to solving a number of problems in astronomy and time-keeping metrology including the search for a stochastic gravitational wave background in the early universe, testing general relativity, and establishing a new time-scale. The full exploration of pulsar properties requires that proper ...

langevin equation for a nano-particle suspended in a laminar fluid flow was analytically studied. the brownian motion generated from molecular bombardment was taken as a wiener stochastic process and approximated by a gaussian white noise. euler-maruyama method was used to solve the langevin equation numerically. the accuracy of brownian simulation was checked by performing a series of simulati...

We deal with a class of reaction-diffusion equations, in space dimension d > 1, perturbed by a Gaussian noise ∂wδ/∂t which is white in time and colored in space. We assume that the noise has a small correlation radius δ, so that it converges to the white noise ∂w/∂t, as δ ↓ 0. By using arguments of Γ-convergence, we prove that, under suitable assumptions, the quasi-potential Vδ converges to the...