Related papers: Effective action for stochastic partial differenti…
Quantum Brownian motion plays a fundamental role in many areas of modern physics. In the path-integral formulation, the environmental quantum fluctuations driving the system dynamics can be characterized by auxiliary stochastic fields. For…
In this chapter we present a general method of constructing the effective equation which describes the behaviour of small-amplitude solutions for a nonlinear PDE in finite volume, provided that the linear part of the equation is a…
In this paper we focus on nonlinear SPDEs with singularities included in both drift and noise coefficients, for which the Gelfand-triple argument developed for (local) monotone SPDEs turns out to be invalid. We propose a general framework…
We work with $\phi^4$ theory and study the 4PI effective action at 3-loop order. We discuss the relationship between the equations of motion obtained by taking functional derivatives of the effective action with respect to the variational…
We propose an approach for calculating one-loop effective actions and vacuum energies in quantum field theory. Spectral functions are functions defined by the eigenvalues of an operator. One-loop effective actions and vacuum energies in…
Semilinear hyperbolic stochastic partial differential equations (SPDEs) find widespread applications in the natural and engineering sciences. However, the traditional Gaussian setting may prove too restrictive, as phenomena in mathematical…
The irreducibility is fundamental for the study of ergodicity of stochastic dynamical systems. The existing methods on the irreducibility of stochastic partial differential equations (SPDEs) and stochastic differential equations (SDEs)…
This paper investigates a Stochastic Partial Differential Equation (SPDE) derived from the Fokker-Planck equation associated with Score-based Generative Models. We modify the standard Fokker-Planck equation to better represent practical…
Fractional calculus provides a rigorous mathematical framework to describe anomalous stochastic processes by generalizing the notion of classical differential equations to their fractional-order counterparts. By introducing the fractional…
For nonsupersymmetric theories, the one-loop effective action can be computed via zeta function regularization in terms of the functional trace of the heat kernel associated with the operator which appears in the quadratic part of the…
Convenient, easy to implement stochastic integration methods are developed on the basis of abstract one-step deterministic order $p$ integration techniques. The abstraction as an arbitrary one step map allows the inspection of easy to…
We consider the stochastic Ginzburg-Landau equation in a bounded domain. We assume the stochastic forcing acts only on high spatial frequencies. The low-lying frequencies are then only connected to this forcing through the non-linear…
In this article we will present a new perspective on the variable order fractional calculus, which allows for differentiation and integration to a variable order, i.e. one differentiates (or integrates) a function along the path of a…
In this work we consider solutions to stochastic partial differential equations with transport noise, which are known to converge, in a suitable scaling limit, to solution of the corresponding deterministic PDE with an additional viscosity…
In this paper, we present a new statistical approach to the problem of incorporating experimental observations into a mathematical model described by linear partial differential equations (PDEs) to improve the prediction of the state of a…
We present the universal one-loop effective action for all operators of dimension up to six obtained by integrating out massive, non-degenerate multiplets. Our general expression may be applied to loops of heavy fermions or bosons, and has…
We prove that a system of locally interacting diffusions carrying discrete masses, subject to an environmental noise and undergoing mass coagulation, converges to a system of Stochastic Partial Differential Equations (SPDEs) with…
Many complex fluids can be described by continuum hydrodynamic field equations, to which noise must be added in order to capture thermal fluctuations. In almost all cases, the resulting coarse-grained stochastic partial differential…
This note deals with existence and uniqueness of (variational) solutions to the following type of stochastic partial differential equations on a Hilbert space H dX(t) = A(t,X(t))dt + B(t,X(t))dW(t) + h(t) dG(t) where A and B are random…
The efficient representation of random fields on geometrically complex domains is crucial for Bayesian modelling in engineering and machine learning. Today's prevalent random field representations are either intended for unbounded domains…