Related papers: Renormalization of stochastic differential equatio…
The macroscopic behavior of dissipative stochastic partial differential equations usually can be described by a finite dimensional system. This article proves that a macroscopic reduced model may be constructed for stochastic…
Power-law noises abound in nature and have been observed extensively in both time series and spatially varying environmental parameters. Although, recent years have seen the extension of traditional stochastic partial differential equations…
We study a class of semi-implicit Taylor-type numerical methods that are easy to implement and designed to solve multidimensional stochastic differential equations driven by a general rough noise, e.g. a fractional Brownian motion. In the…
The long term aim is to use modern dynamical systems theory to derive discretisations of noisy, dissipative partial differential equations. As a first step we here consider a small domain and apply stochastic centre manifold techniques to…
A recently developed renormalization approach is used to study the electron-phonon coupling in many-electron systems. By starting from an Hamiltonian which includes a small gauge symmetry breaking field, we directly derive a BCS-like…
Constructing numerical models of noisy partial differential equations is very delicate. Our long term aim is to use modern dynamical systems theory to derive discretisations of dissipative stochastic partial differential equations. As a…
We develop strategies for enhancing the signal/noise ratio for stochastically sampled correlation functions. The techniques are general and offer a wide range of applicability. We demonstrate the potential of the approach with a generic…
The focus of this paper is on stochastic variational inequalities (VI) under Markovian noise. A prominent application of our algorithmic developments is the stochastic policy evaluation problem in reinforcement learning. Prior…
There are two possible methods for the inclusion of the chemical potential in a relativistic bosonic field theory. The most popular method has recently been criticised by some authors, so much so as to require a re-analysis of the entire…
This paper develops a quantitative framework for analyzing the mean-square exponential stabilization of stochastic linear systems with multiplicative noise, focusing specifically on the optimal stabilizing rate, which characterizes the…
We study periodic solutions to the following divergence-form stochastic partial differential equation with Wick-renormalized gradient on the $d$-dimensional flat torus $\mathbb{T}^d$, \[ -\nabla\cdot\left(e^{\diamond (- \beta X)…
A non-perturbative method which can go beyond the weak coupling perturbation theory is introduced. Essential idea is to formulate a set of exact differential equations as a function of the coupling strength $g$. Unlike other resummation in…
We propose a fast and scalable optimization method to solve chance or probabilistic constrained optimization problems governed by partial differential equations (PDEs) with high-dimensional random parameters. To address the critical…
Multiplicative noise models are often used instead of additive noise models in cases in which the noise variance depends on the state. Furthermore, when Poisson distributions with relatively small counts are approximated with normal…
We study the mechanism of stochastic resonance in a two dimensional Landau Ginzburg equation perturbed by a white noise. We shortly review how to renormalize the equation in order to avoid ultraviolet divergences. Next we show that the…
Motivated by studies of indirect measurements in quantum mechanics, we investigate stochastic differential equations with a fixed point subject to an additional infinitesimal repulsive perturbation. We conjecture, and prove for an important…
In this paper, we extend our research concerning the standard and linearized monotonicity methods for the inverse problem of the time harmonic elastic wave equation and introduce the modification of these methods for noisy data. In more…
We present a theory for the construction of renormalized kinetic equations to describe the dynamics of classical systems of particles in or out of equilibrium. A closed, self-consistent set of evolution equations is derived for the…
We develop a computational procedure to estimate the covariance hyperparameters for semiparametric Gaussian process regression models with additive noise. Namely, the presented method can be used to efficiently estimate the variance of the…
We present a new numerical method for accurate computations of solutions to (linear) one dimensional Schr\"odinger equations with periodic potentials. This is a prominent model in solid state physics where we also allow for perturbations by…