Approximative Theorem of Incomplete Riemann-Stieltjes Sum of Stochastic Integral

2018/03/14 by Jingwei Liu, Liu, Jingwei
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Mathematical functions and polynomials #Numerical Analysis (math.NA) #Probability (math.PR) #Stochastic processes and financial applications #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1803.05182

openalex publication_date 2018/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The approximative theorems of incomplete Riemann-Stieltjes sums of Ito stochastic integral, mean square integral and Stratonovich stochastic integral with respect to Brownian motion are investigated. Some sufficient conditions of incomplete Riemann-Stieltjes sums approaching stochastic integral are developed, which establish the alternative ways to converge stochastic integral. And, Two simulation examples of incomplete Riemann-Stieltjes sums about Ito stochastic integral and Stratonovich stochastic integral are given for demonstration.

Citations

• An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations

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