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Mathematics > Probability

arXiv:1803.05182 (math)
[Submitted on 14 Mar 2018 (v1), last revised 17 Mar 2018 (this version, v2)]

Title:Approximative Theorem of Incomplete Riemann-Stieltjes Sum of Stochastic Integral

Authors:Jingwei Liu
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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.
Comments: 4 figures
Subjects: Probability (math.PR); Numerical Analysis (math.NA)
Cite as: arXiv:1803.05182 [math.PR]
  (or arXiv:1803.05182v2 [math.PR] for this version)
  https://doi.org/10.48550/arXiv.1803.05182

Submission history

From: Jingwei Liu [view email]
[v1] Wed, 14 Mar 2018 09:56:47 UTC (17 KB)
[v2] Sat, 17 Mar 2018 07:12:42 UTC (18 KB)
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