Related papers: Symmetry of stochastic equations
We discuss some recent advances concerning the symmetry of stochastic differential equations, and in particular the interrelations between these and the integrability -- complete or partial -- of the equations.
An algorithmic method to exploit a general class of infinitesimal symmetries for reducing stochastic differential equations is presented and a natural definition of reconstruction, inspired by the classical reconstruction by quadratures, is…
The Monotonicity inequality is an important tool in the understanding of existence and uniqueness of strong solutions for Stochastic PDEs. In this article, we discuss three approaches to establish this deterministic inequality explicitly.
Stochastic diffusion equations are crucial for modeling a range of physical phenomena influenced by uncertainties. We introduce the generalized finite difference method for solving these equations. Then, we examine its consistency,…
We examine the Lie symmetries of a semi-linear partial differential equations and their connections to the analogous symmetries of the forward-backward stochastic differential equations (FBSDEs), established through the generalized…
We discuss the role and merits of symmetry methods for the analysis of biological systems. In particular, we consider systems of first order ordinary differential equations and provide a comprehensive review of the geometrical foundations…
The Fokker-Planck equation needs to be modified when the diffusion parameters are not constant, in order to match it with the backward equation. It even becomes simpler, and the integration of the underlying stochastic differential equation…
The study of symmetries of partial differential equations (PDEs) has been traditionally treated as a geometrical problem. Although geometrical methods have been proven effective with regard to finding infinitesimal symmetry transformations,…
We extend two of the methods previously introduced to find discrete symmetries of differential equations to the case of difference and differential-difference equations. As an example of the application of the methods, we construct the…
We discuss W-symmetries of Ito stochastic differential equations, introduced in a recent paper by Gaeta and Spadaro [J. Math. Phys. 2017]. In particular, we discuss the general form of acceptable generators for continuous (Lie-point)…
These lecture notes provide an introduction to the theory and application of symmetry methods for ordinary differential equations, building on minimal prerequisites. Their primary purpose is to enable a quick and self-contained approach for…
Covariance of the resulting probabilities requires the "anti-Ito" sense. The corresponding Fokker-Planck equation is simplified and preserves important features of the case with a constant diffusion. Multiplicative noise can always be…
In some cases, solutions to nonlinear PDEs happen to be asymptotically (for large $x$ and/or $t$) invariant under a group $G$ which is not a symmetry of the equation. After recalling the geometrical meaning of symmetries of differential…
For partial differential equations (PDEs) that have $n\geq2$ independent variables and a symmetry algebra of dimension at least $n-1$, an explicit algorithmic method is presented for finding all symmetry-invariant conservation laws that…
A supersymmetric method for the construction of so-called conditionally exactly solvable quantum systems is reviewed and extended to classical stochastic dynamical systems characterized by a Fokker-Planck equation with drift. A class of…
The existence and uniqueness of measure-valued solutions to stochastic nonlinear, non-local Fokker-Planck equations is proven. This type of stochastic PDE is shown to arise in the mean field limit of weakly interacting diffusions with…
The concept of symmetries in physics is briefly reviewed. In the first part of these lecture notes, some of the basic mathematical tools needed for the understanding of symmetries in nature are presented, namely group theory, Lie groups and…
The interpretation of numerical methods, such as finite difference methods for differential equations, as point estimators suggests that formal uncertainty quantification can also be performed in this context. Competing statistical…
Symmetry is an important feature of many constraint programs. We show that any symmetry acting on a set of symmetry breaking constraints can be used to break symmetry. Different symmetries pick out different solutions in each symmetry…
The construction and role of symmetries for difference equations are now well known. In this paper, the symmetry analysis of the discrete Painleve equations is considered. We assume that the characteristics depend on $n$ and $u_n$ only and…