Related papers: Stochastic trace formulas
We show that the Schr\"{o}dinger-Newton equation, which describes the nonlinear time evolution of self-gravitating quantum matter, can be made compatible with the no-signaling requirement by elevating it to a stochastic differential…
The not necessarily unitary evolution operator of a finite dimensional quantum system is studied with the help of a projection operators technique. Applying this approach to the Schr\"odinger equation allows the derivation of an alternative…
A parameter estimation problem is considered for a stochastic parabolic equation with multiplicative noise under the assumption that the equation can be reduced to an infinite system of uncoupled diffusion processes. From the point of view…
We investigate the stochastic resonance phenomenon in a physical system based on a tunnel diode. The experimental control parameters are set to allow the control of the frequency and amplitude of the deterministic modulating signal over an…
Reconstructing noise-driven nonlinear networks from time series of output variables is a challenging problem, which turns to be very difficult when nonlinearity of dynamics, strong noise impacts and low measurement frequencies jointly…
We consider statistics for stochastic evolution equations in Hilbert space with emphasis on stochastic partial differential equations (SPDEs). We observe a solution process under additional measurement errors and want to estimate a real or…
An approach to stochastic evolution equations based on a simple generalization of known embedding theorems is presented. It allows for the inclusion of problems which have nonlinear non monotone operators. This is used to discuss the…
We present a consistent method to calculate the probability distribution of soliton parameters in systems with additive noise. Even though a weak noise is considered, we are interested in probabilities of large fluctuations (generally…
A stochastic affine evolution equation with bilinear noise term is studied where the driving process is a real-valued fractional Brownian motion. Stochastic integration is understood in the Skorokhod sense. Existence and uniqueness of weak…
In this paper, we study the motion by mean curvature of curves in the plane perturbed by scale-dependent noise. We first introduce a so-called scale-dependent noise from the physics background to the curve shortening flow. To be more…
Doubly nonlinear stochastic evolution equations are considered. Upon assuming the additive noise to be rough enough, we prove the existence of probabilistically weak solutions of Friedrichs type and study their uniqueness in law. This…
The non-linear dynamics of long-wavelength cosmological fluctuations may be phrased in terms of an effective classical, but stochastic evolution equation. The stochastic noise represents short-wavelength modes that continually redshift into…
Statistical inference for a linear stochastic hyperbolic equation with two unknown parameters is studied. Based on observation of coordinates of the solution or their linear combination, minimum contrast estimators are introduced. Strong…
The parameterization method (PM) provides a broad theoretical and numerical foundation for computing invariant manifolds of dynamical systems. PM implements a change of variables in order to represent trajectories of a system of ordinary…
The solution of a parabolic stochastic partial differential equation (SPDE) driven by an infinite-dimensional Brownian motion is in general not a semi-martingale anymore and does in general not satisfy an It\^{o} formula like the solution…
The problem of nonlinear filtering of a random field observed in the presence of a noise, modeled by a persistent fractional Brownian sheet of Hurst index $(H_1,H_2)$ with $0.5<H_1,H_2<1$, is studied and a suitable version of the Bayes'…
Energy level statistics of quantized chaotic systems have been evaluated in the semiclassical limit via their periodic orbits using the Gutzwiller and related trace formulae. Here we evaluate a spectral statistic of chaotic 4-regular…
We investigate the problem of joint statistical estimation of several parameters for a stochastic differential equation driven by an additive fractional Brownian motion. Based on discrete-time observations of the model, we construct an…
We study the statistical properties of stochastic evolution equations driven by space-only noise, either additive or multiplicative. While forward problems, such as existence, uniqueness, and regularity of the solution, for such equations…
The archetypal system demonstrating stochastic resonance is nothing more than a threshold triggered device. It consists of a periodic modulated input and noise. Every time an output crosses the threshold the signal is recorded. Such a…