Approximative Theorem of Incomplete Riemann-Stieltjes Sum of Stochastic Integral
For researchers in stochastic calculus, this provides incremental theoretical extensions to existing convergence results for stochastic integrals.
The paper develops sufficient conditions for incomplete Riemann-Stieltjes sums to converge to Ito and Stratonovich stochastic integrals, providing alternative convergence methods. Simulation examples demonstrate the theoretical results.
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.