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Applicable Analysis
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Volume 99, 2020 - Issue 6
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Articles

Rough path analysis for local time of G-Brownian motion

Litan YanDepartment of Mathematics, College of Science, Donghua University, Shanghai, People's Republic of ChinaCorrespondence[email protected]
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,
Yumiao LiDepartment of Mathematics, College of Science, Donghua University, Shanghai, People's Republic of ChinaView further author information
&
Kun HeDepartment of Mathematics, College of Science, Donghua University, Shanghai, People's Republic of ChinaView further author information
Pages 899-921 | Received 16 Oct 2017, Accepted 10 Aug 2018, Published online: 27 Aug 2018

References

  • Peng S. G-expectation, G-Brownian motion and related stochastic calculus of Itô type. Stoch Anal Appl Abel Symp. 2007;2:51–567.
  • Peng S. Nonlinear expections and stochastic calculus under uncertainty. 2010. arXiv:1002.4546. Available from: http://front.math.ucdavis.edu/1002.4546
  • Denis L, Hu M, Peng S. Function spaces and capacity related to a sublinear expectation: application to G-Brownian motion pathes. Potential Anal. 2011;34:139–161. doi: 10.1007/s11118-010-9185-x
  • Li X, Peng S. Stopping times and Related Itô Calculus with G-Brownian motion. Stoch Process Appl. 2011;121:1492–1508. doi: 10.1016/j.spa.2011.03.009
  • Peng S, Song Y. G-expectation weighted Sobolev spaces, backward SDE and path dependent PDE. J Math Soc Jpn. 2015;67:1725–1757. doi: 10.2969/jmsj/06741725
  • Hu M, Wang F, Zheng G. Quasi-continuous random variables and processes under the G-expectation framework. Stoch Process Appl. 2016;126:2367–2387. doi: 10.1016/j.spa.2016.02.003
  • Hu M, Ji S. Stochastic maximum principle for stochastic recursive optimal control problem under volatility ambiguity. SIAM J Control Optim. 2016;54:918–945. doi: 10.1137/15M1037639
  • Li X, Lin X, Lin Y. Lyapunov-type conditions and stochastic differential equations driven by G-Brownian motion. J Math Anal Appl. 2016;439:235–255. doi: 10.1016/j.jmaa.2016.02.042
  • Li X, Lin Y. Generalized Wasserstein distance and weak convergence of sublinear expectations. J Theor Prob. 2017;30:581–593. doi: 10.1007/s10959-015-0651-7
  • Li Y, Yan L. Stability of delayed Hopfield neural networks under a sub-linear expectation framework. J Franklin Inst. 2018;355:4268–4281. doi: 10.1016/j.jfranklin.2018.04.007
  • Yan L, Zhang Q, Gao B. Hilbert transform of G-Brownian local time. Stoch Dyn. 2014;14:1450006. (26 pages). doi: 10.1142/S0219493714500063
  • Hu M, Peng S. On representation theorem of G-expectations and paths of G-Brownian motion. Acta Math Sin Engl Ser. 2009;25:1–8.
  • Peng S. Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation. Stoch Process Appl. 2008;118:2223–2253. doi: 10.1016/j.spa.2007.10.015
  • Geng X, Qian Z, Yang D. G-Brownian motion as rough paths and differential equations driven by G-Brownian motion. Séminaire de Probabilités Vol. XLVI. Springer; 2014. p. 125–193. (Lect. Notes in Math.; 2123).
  • Peng S, Zhang H. Stochastic calculus with respect to G-Brownian motion viewed through rough paths. Sci China Math. 2017;60:1–20. doi: 10.1007/s11425-016-0171-4
  • Lin Q. Local time and Tanaka formula for the G-Brownian motion. J Math Anal Appl. 2013;398:315–334. doi: 10.1016/j.jmaa.2012.09.001
  • Yan L, Sun X, Gao B. Integration with respect to the G-Brownian local time. J Math Anal Appl. 2015;424:835–860. doi: 10.1016/j.jmaa.2014.11.046
  • Feng C, Zhao H. Two-parameter p,q-variation path and integration of local times. Potential Anal. 2006;25:165–204. doi: 10.1007/s11118-006-9024-2
  • Feng C, Zhao H. Local time rough path for Lévy processes. Electron J Probab. 2010;15:452–483. doi: 10.1214/EJP.v15-770
  • Lyons T, Qian Z. System control and rough paths. Oxford: Clarendon Press; 2002.
  • Ryan RA. Introduction to tensor products of banach spaces. London: Springer-Verlag; 2002.
  • Dudley RM, Norvaiša R. An introduction to p-variation and Young integrals. Lecture Notes Series 1998. MaPhySto: http://www.maphysto.dk/oldpages/publications/publications1998_static.html

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