RETRACTED: Sensitivity Analysis Based on Markovian Integration by Parts Formula
Abstract
:1. Introduction
2. Formulation and Main Results
3. Proof of Propositions 1 and 2
3.1. Case :
3.2. Case (b):
4. Numerical Simulation of Simple Examples with Two-State Markov Chains
Acknowledgments
Author Contributions
Conflicts of Interest
Appendix A. Extension to Non-Differentiable Function ϕ(·)
- (i)
- First, suppose , we show that
- (ii)
- For , we prove Equation (A1). Since is differentiable with respect to when , the conclusion in Section 3.1 is valid on the set . By Equations (A6) and (A7) we have
- (iii)
- Finally, we extend from to the class . Clearly, can be a.e. approximated by a sequence s.t.
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Hang, Y.; Liu, Y.; Xu, X.; Chen, Y.; Mo, S. RETRACTED: Sensitivity Analysis Based on Markovian Integration by Parts Formula. Math. Comput. Appl. 2017, 22, 40. https://doi.org/10.3390/mca22040040
Hang Y, Liu Y, Xu X, Chen Y, Mo S. RETRACTED: Sensitivity Analysis Based on Markovian Integration by Parts Formula. Mathematical and Computational Applications. 2017; 22(4):40. https://doi.org/10.3390/mca22040040
Chicago/Turabian StyleHang, Yongsheng, Yue Liu, Xiaoyang Xu, Yan Chen, and Shu Mo. 2017. "RETRACTED: Sensitivity Analysis Based on Markovian Integration by Parts Formula" Mathematical and Computational Applications 22, no. 4: 40. https://doi.org/10.3390/mca22040040