Discrete It\^o Formulas and Their Applications to Stochastic Numerics

TL;DR

This paper surveys the author's observations on discrete-time analogues of Itô formulas and explores their applications in stochastic numerical methods.

Contribution

It introduces and discusses discrete Itô formulas and highlights their applications in stochastic numerical analysis.

Findings

Discrete Itô formulas extend continuous Itô calculus to discrete settings.

Applications include improved stochastic numerical algorithms.

Provides insights into discrete stochastic calculus techniques.

Abstract

This is a survey note of the author's observations on the discrete-time analogues of It\^o formulas.