Related papers: Stochastic quantization with discrete fictitious t…
In this paper, adaptive estimation based on noisy quantized observations is studied. A low complexity adaptive algorithm using a quantizer with adjustable input gain and offset is presented. Three possible scalar models for the parameter to…
We consider a quantization of relativistic wave equations which allows to treat quantum fields together with interacting particles at a finite time. We discuss also a dissipative interaction with the environment. We introduce a stochastic…
We study the long-time behavior of fully discretized semilinear SPDEs with additive space-time white noise, which admit a unique invariant probability measure $\mu$. We show that the average of regular enough test functions with respect to…
Using stochastic quantization method we derive equations for correlators of quantum fluctuations around the classical solution in the massless phi^4 theory. The obtained equations are then solved in the lowest orders of perturbation theory,…
We present a new method to renormalize stochastic differential equations subjected to multiplicative noise. The method is based on the widely used concept of effective potential in high energy physics, and has already been successfully…
We extend stochastic basis adaptation and spatial domain decomposition methods to solve time varying stochastic partial differential equations (SPDEs) with a large number of input random parameters. Stochastic basis adaptation allows the…
A system under constant observation is practically freezed to the measurement subspace. If the system driving is a random classical field, the survival probability of the system in the subspace becomes a random variable described by the…
We introduce symplectic quantization, a novel functional approach to quantum field theory which allows to sample quantum fields fluctuations directly in Minkowski space-time, at variance with the traditional importance sampling protocols,…
The concept of the random discretization of the space-time is suggested. It is the way to consistent compatible synthesis of quantum and relativistic principles and principle of geometrization. The basic idea of this concept is physical…
We use a probabilistic method to describe the effect of laser noise on the laser-atom interaction, in the case that the atom is a two level system without spontaneous emission. The stochastic differential equation for the laser-atom…
It has recently been observed that a stochastic (infinite degree of freedom) time series with a $1/f^\alpha$ power spectrum can exhibit a finite correlation dimension, even for arbitrarily large data sets. [A.R. Osborne and A.~Provenzale,…
We propose and analyse a new type of fully discrete finite element approximation of a class of linear stochastic parabolic evolution equations with additive noise. Our discretization differs from previous ones in that we use a finite…
For optimizing a non-convex function in finite dimension, a method is to add Brownian noise to a gradient descent, allowing for transitions between basins of attractions of different minimizers. To adapt this for optimization over a space…
We study the Langevin dynamics of a U(1) lattice gauge theory on the torus, and prove that they converge for short time in a suitable gauge to a system of stochastic PDEs driven by space-time white noises. This also yields convergence of…
We propose a method of data quantization of finite discrete-time signals which optimizes the error estimate of low frequency Haar coefficients. We also discuss the error/noise bounds of this quantization in the Fourier space. Our result…
In this paper we investigate a nonlinear stochastic partial differential equation (spde in short) perturbed by a space-correlated Gaussian noise in arbitrary dimension $d\geq1$, with a non-Lipschitz coefficient noisy term. The equation…
We develop and analyze a numerical method for stochastic time-fractional diffusion driven by additive fractionally integrated Gaussian noise. The model involves two nonlocal terms in time, i.e., a Caputo fractional derivative of order…
In the context of unitary evolution of a generic quantum system interrupted at random times with non-unitary evolution due to interactions with either the external environment or a measuring apparatus, we adduce a general theoretical…
We study a nonlinear stochastic heat equation forced by a space-time white noise on closed surfaces, with nonlinearity $e^{\beta u}$. This equation corresponds to the stochastic quantization of the Liouville quantum gravity (LQG) measure.…
We propose here a new symplectic quantization scheme, where quantum fluctuations of a scalar field theory stem from two main assumptions: relativistic invariance and equiprobability of the field configurations with identical value of the…