- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Advances in Mathematical Physics
Volume 2013 (2013), Article ID 827192, 11 pages
The -Transform of Sub-fBm and an Application to a Class of Linear Subfractional BSDEs
1College of Information Science and Technology, Donghua University, 2999 North Renmin Road, Songjiang, Shanghai 201620, China
2School of Sciences, Ningbo University of Technology, 201 Fenghua Road, Ningbo 315211, China
3Department of Mathematics, College of Science, Donghua University, 2999 North Renmin Road, Songjiang, Shanghai 201620, China
Received 28 May 2013; Revised 7 June 2013; Accepted 8 June 2013
Academic Editor: Ming Li
Copyright © 2013 Zhi Wang and Litan Yan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- T. Bojdecki, L. G. Gorostiza, and A. Talarczyk, “Sub-fractional Brownian motion and its relation to occupation times,” Statistics & Probability Letters, vol. 69, no. 4, pp. 405–419, 2004.
- T. Bojdecki, L. G. Gorostiza, and A. Talarczyk, “Some extensions of fractional Brownian motion and sub-fractional Brownian motion related to particle systems,” Electronic Communications in Probability, vol. 12, pp. 161–172, 2007.
- E. Alòs, O. Mazet, and D. Nualart, “Stochastic calculus with respect to Gaussian processes,” The Annals of Probability, vol. 29, no. 2, pp. 766–801, 2001.
- D. Nualart, The Malliavin Calculus and Related Topics, Springer, Berlin, Germany, 2nd edition, 2006.
- T. Bojdecki, L. G. Gorostiza, and A. Talarczyk, “Fractional Brownian density process and its self-intersection local time of order ,” Journal of Theoretical Probability, vol. 17, no. 3, pp. 717–739, 2004.
- J. Liu and L. Yan, “Remarks on asymptotic behavior of weighted quadratic variation of subfractional Brownian motion,” Journal of the Korean Statistical Society, vol. 41, no. 2, pp. 177–187, 2012.
- G. Shen and C. Chen, “Stochastic integration with respect to the sub-fractional Brownian motion with ,” Statistics & Probability Letters, vol. 82, no. 2, pp. 240–251, 2012.
- C. Tudor, “Some properties of the sub-fractional Brownian motion,” Stochastics, vol. 79, no. 5, pp. 431–448, 2007.
- C. Tudor, “Inner product spaces of integrands associated to subfractional Brownian motion,” Statistics & Probability Letters, vol. 78, no. 14, pp. 2201–2209, 2008.
- C. Tudor, “Some aspects of stochastic calculus for the sub-fractional Brownian motion,” Analele Universitatii Bucuresti. Matematica, vol. 57, no. 2, pp. 199–230, 2008.
- C. Tudor, “On the Wiener integral with respect to a sub-fractional Brownian motion on an interval,” Journal of Mathematical Analysis and Applications, vol. 351, no. 1, pp. 456–468, 2009.
- L. Yan, K. He, and C. Chen, “The generalized Bouleau-Yor identity for a sub-fractional Brownian motion,” Science China Mathematics, 2013.
- L. Yan and G. Shen, “On the collision local time of sub-fractional Brownian motions,” Statistics & Probability Letters, vol. 80, no. 5-6, pp. 296–308, 2010.
- L. Yan, G. Shen, and K. He, “Itô's formula for a sub-fractional Brownian motion,” Communications on Stochastic Analysis, vol. 5, no. 1, pp. 135–159, 2011.
- É. Pardoux and S. G. Peng, “Adapted solution of a backward stochastic differential equation,” Systems & Control Letters, vol. 14, no. 1, pp. 55–61, 1990.
- S. Peng, “Backward stochastic differential equations,” in Nonlinear Expectations, Nonlinear Evaluations and Risk Measures, Lecture Notes in Chinese Summer School in Mathematics Weihai, 2004.
- F. Biagini, Y. Hu, B. Øksendal, and A. Sulem, “A stochastic maximum principle for processes driven by fractional Brownian motion,” Stochastic Processes and their Applications, vol. 100, pp. 233–253, 2002.
- C. Bender, “Explicit solutions of a class of linear fractional BSDEs,” Systems & Control Letters, vol. 54, no. 7, pp. 671–680, 2005.
- Y. Hu and S. Peng, “Backward stochastic differential equation driven by fractional Brownian motion,” SIAM Journal on Control and Optimization, vol. 48, no. 3, pp. 1675–1700, 2009.
- J.-M. Bismut, “Conjugate convex functions in optimal stochastic control,” Journal of Mathematical Analysis and Applications, vol. 44, pp. 384–404, 1973.
- C. Geiss, S. Geiss, and E. Gobet, “Generalized fractional smoothness and -variation of BSDEs with non-Lipschitz terminal condition,” Stochastic Processes and their Applications, vol. 122, no. 5, pp. 2078–2116, 2012.
- N. El Karoui, S. Peng, and M. C. Quenez, “Backward stochastic differential equations in finance,” Mathematical Finance, vol. 7, no. 1, pp. 1–71, 1997.
- J. Ma, P. Protter, and J. M. Yong, “Solving forward-backward stochastic differential equations explicitly—a four step scheme,” Probability Theory and Related Fields, vol. 98, no. 3, pp. 339–359, 1994.
- L. Maticiuc and T. Nie, “Fractional backward stochastic differential equations and fractional backward variational inequalities,” http://arxiv.org/abs/1102.3014.
- S. G. Peng, “Backward stochastic differential equations and applications to optimal control,” Applied Mathematics and Optimization, vol. 27, no. 2, pp. 125–144, 1993.
- B. B. Mandelbrot and J. W. van Ness, “Fractional Brownian motions, fractional noises and applications,” SIAM Review, vol. 10, pp. 422–437, 1968.
- F. Biagini, Y. Hu, B. Øksendal, and T. Zhang, Stochastic Calculus for Fractional Brownian Motion and Applications, Springer, London, UK, 2006.
- Y. Hu, “Integral transformations and anticipative calculus for fractional Brownian motions,” Memoirs of the American Mathematical Society, vol. 175, no. 825, 2005.
- Y. S. Mishura, Stochastic Calculus for Fractional Brownian Motion and Related Processes, Springer, Berlin, Germany, 2008.
- M. Li, “On the long-range dependence of fractional Brownian motion,” Mathematical Problems in Engineering, vol. 2013, Article ID 842197, 5 pages, 2013.
- M. Li and W. Zhao, “On noise,” Mathematical Problems in Engineering, vol. 2012, Article ID 673648, 23 pages, 2012.
- M. Li and W. Zhao, “Quantitatively investigating locally weak stationarity of modified multifractional Gaussian noise,” Physica A, vol. 391, no. 24, pp. 6268–6278, 2012.
- S. C. Lim and S. V. Muniandy, “On some possible generalizations of fractional Brownian motion,” Physics Letters A, vol. 266, no. 2-3, pp. 140–145, 2000.
- M. Zähle, “Integration with respect to fractal functions and stochastic calculus. I,” Probability Theory and Related Fields, vol. 111, no. 3, pp. 333–374, 1998.
- C. Bender, “An -transform approach to integration with respect to a fractional Brownian motion,” Bernoulli, vol. 9, no. 6, pp. 955–983, 2003.
- C. Bender, “An Itô formula for generalized functionals of a fractional Brownian motion with arbitrary Hurst parameter,” Stochastic Processes and their Applications, vol. 104, no. 1, pp. 81–106, 2003.