Related papers: Stochastic quantization with discrete fictitious t…
We propose a high-dimensional white noise test that captures serial correlations within and across component series without specifying an alternative model. The test statistic is a U-statistic based on sample autocovariances. Under the…
Even though measurement results obtained in the real world are generally both noisy and continuous, quantum measurement theory tends to emphasize the ideal limit of perfect precision and quantized measurement results. In this article, a…
In this paper we present a rigorous asymptotic analysis for stochastic systems with two fast relaxation times. The mathematical model analyzed in this paper consists of a Langevin equation for the particle motion with time-dependent force…
Simulations of quantum systems with Hamiltonian classical stochastic noise can be challenging when the noise exhibits temporal correlations over a multitude of time scales, such as for $1/f$ noise in solid-state quantum information…
Using ideas from paracontrolled calculus, we prove local well-posedness of a renormalized version of the three-dimensional stochastic nonlinear wave equation with quadratic nonlinearity forced by an additive space-time white noise on a…
We study strictly parabolic stochastic partial differential equations on $\R^d$, $d\ge 1$, driven by a Gaussian noise white in time and coloured in space. Assuming that the coefficients of the differential operator are random, we give…
We prove uniform synchronisation by noise with rates for the stochastic quantisation equation in dimensions two and three. The proof relies on a combination of coming down from infinity estimates and the framework of order-preserving Markov…
In this work we analyze the stochastic dynamics of the Kauffman model evolving under the influence of noise. By considering the average crossing time between two distinct trajectories, we show that different Kauffman models exhibit a…
An experimental test of the "special state" theory of quantum measurement is proposed. It should be feasible with present-day laboratory equipment and involves a slightly elaborated Stern-Gerlach setup. The "special state" theory is…
The theory of quasifree quantum stochastic calculus for infinite-dimensional noise is developed within the framework of Hudson-Parthasarathy quantum stochastic calculus. The question of uniqueness for the covariance amplitude with respect…
We study the nonparametric change point estimation for common changes in the means of panel data. The consistency of estimates is investigated when the number of panels tends to infinity but the sample size remains finite. Our focus is on…
This paper studies the nonlinear one-dimensional stochastic heat equation driven by a Gaussian noise which is white in time and which has the covariance of a fractional Brownian motion with Hurst parameter 1/4\textless{}H\textless{}1/2 in…
Even in large systems, the effect of noise arising from when populations are initially small can persist to be measurable on the macroscale. A deterministic approximation to a stochastic model will fail to capture this effect, but it can be…
We consider the influence of stochastic perturbations on stability of a unique positive equilibrium of a difference equation subject to prediction-based control. These perturbations may be multiplicative $$x_{n+1}=f(x_n)-\left( \alpha +…
We study the effect of local unitary noise on the entanglement evolution of a two-qubit system subject to local monitoring and inter-qubit coupling. We construct a stochastic Hamiltonian by incorporating the noise into the…
We investigate stochastic quantization as a method to go from a classical PDE (with stochastic time $\lambda$) to a corresponding quantum theory in the limit $\lambda\to\infty$. We test the method for a linear PDE satisfied by the free…
Spatiotemporal evolution in the real Ginzburg-Landau equation is studied with space-time noise and a slowly increasing critical parameter. Analytical estimates for the characteristic size of the domains formed in a slow sweep through the…
We argue that to solve the foundational problems of quantum theory one has to first understand what it means to quantize a classical system. We then propose a quantization method based on replacement of deterministic c-numbers by…
Wright's delay differential equation is one of the prime examples of a fully nonlinear equation without an explicit solution and whose dynamics can be understood by analytic means. In this paper, we introduce stochastic perturbations by…
An elementary prediction of the quantization of the gravitational field is that the Newtonian interaction can entangle pairs of massive objects. Conversely, in models of gravity in which the field is not quantized, the gravitational…