Abstract
AbstractIn this paper, we tame the uncertainty about the volatility in time-averaging principle for stochastic differential equations driven by G-Brownian motion (G-SDEs) based on the Lyapunov condition. That means we treat the time-averaging principle for stochastic differential equations based on the Lyapunov condition in the presence of a family of probability measures, each corresponding to a different scenario for the volatility. The main tool for the mathematical analysis is the G-stochastic calculus, which is introduced in the book by Peng (Nonlinear Expectations and Stochastic Calculus Under Uncertainty. Springer, Berlin, 2019). We show that the solution of a standard equation converges to the solution of the corresponding averaging equation in the sense of sublinear expectation with the help of some properties of G-stochastic calculus. Numerical results obtained using PYTHON illustrate the efficiency of the averaging method.
Funder
National Outstanding Youth Science Fund Project of National Natural Science Foundation of China
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
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