# W-Symmetries of Ito stochastic differential equations

## TL;DR

This paper explores W-symmetries in Ito stochastic differential equations, linking them to conformal groups and demonstrating their role in integrating stochastic equations, extending traditional symmetry methods.

## Contribution

It characterizes the form of W-symmetries for Ito equations and shows how they can be used to facilitate integration, broadening the scope of symmetry analysis in stochastic calculus.

## Key findings

- W-symmetries relate to the linear conformal group.
- W-symmetries can aid in integrating Ito stochastic equations.
- Extends symmetry methods to more general stochastic equations.

## Abstract

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) W-symmetry, arguing they are related to the (linear) conformal group, and how W-symmetries can be used in the integration of Ito stochastic equations along Kozlov theory for standard (deterministic or random) symmetries. It turns out this requires, in general, to consider more general classes of stochastic equations than just Ito ones.