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Tytuł artykułu

Backward stochastic variational inequalities driven by multidimensional fractional Brownian motion

Treść / Zawartość
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We study the existence and uniqueness of the backward stochastic variational inequalities driven by m-dimensional fractional Brownian motion with Hurst parameters Hk (k = 1,... m) greater than 1/2. The stochastic integral used throughout the paper is the divergence type integral.
Rocznik
Strony
307--326
Opis fizyczny
Bibliogr. 21 poz.
Twórcy
autor
  • Nicolaus Copernicus University Faculty of Mathematics and Computer Science ul. Chopina 12/18, 87-100 Toruń, Poland
  • University of Science and Technology Institute of Mathematics and Physics al. prof. S. Kaliskiego 7, 85-796 Bydgoszcz, Poland
Bibliografia
  • [1] V. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces, Ed. Academiei Romane and Noordhoff International Publishing, 1976.
  • [2] C. Bender, Explicit solutions of a class of linear fractional BSDEs, Systems Control Lett. 54 (2005) 7, 671-680.
  • [3] F. Biagini, Y. Hu, B. 0ksendal, A. Sulem, A stochastic maximum principle for processes driven by fractional Brownian motion, Stochastic Process. Appl. 100 (2002) 1, 233-253.
  • [4] D. Borkowski, K. Jańczak-Borkowska, Generalized backward stochastic variational inequalities driven by a fractional Brownian motion, Braz. J. Probab. Stat. 30 (2016) 3, 502-519.
  • [5] D. Borkowski, K. Jańczak-Borkowska, BSDE driven by a multidimensional fractional Brownian motion, submitted.
  • [6] H. Brezis, Operateurs maximaux monotones et semigroupes de contractions dans les spaces de Hilbert, North-Holland Publ. Co., 1973.
  • [7] W. Dai, C.C. Heyde, ltd formula with respect to fractional Brownian motion and its application, J. Appl. Math. Stoch. Anal. 9 (1990), 439-448.
  • [8] L. Decreusefond, A.S. Ustunel, Stochastic analysis of the fractional Brownian motion, Potential Anal. 10 (1998), 177-214.
  • [9] T.E. Duncan, Y. Hu, B. Pasik-Duncan, Stochastic calculus for fractional Brownian motions. I. Theory, SIAM J. Control Optim. 38 (2000), 582-612.
  • [10] Y. Hu, Integral transformations and anticipative calculus for fractional Brownian motions, Mem. Amer. Math. Soc. 175 (2005) 825.
  • [11] Y. Hu, B. 0ksendal, Fractional white noise calculus and application to finance, Inlin. Dimens. Anal. Quantum Probab. Relat. Top. 6 (2003), 1-32.
  • [12] Y. Hu, S. Peng, Backward stochastic differential equation driven by fractional Brownian motion, Siam J. Control Optim. 48 (2009) 3, 1675-1700.
  • [13] K. Jańczak-Borkowska, Generalized BSDEs driven by fractional Brownian motion, Statist. Probab. Lett. 83 (2013) 3, 805-811.
  • [14] S.J. Lin, Stochastic analysis of fractional Brownian motions, Stochastics Stochastics Rep. 55 (1995), 121-140.
  • [15] L. Maticiuc, T. Me, Fractional backward stochastic differential equations and fractional backward variational inequalities, J. Theoret. Probab. 28 (2015) 1, 337-395.
  • [16] L. Maticiuc, A. Ra§canu, A stochastic approach to a multivalued Dirichlet-Neumann problem, Stochastic Process. Appl. 120 (2010) 6, 777-800.
  • [17] J. Miao, X. Yang, Solutions to BSDEs driven by multidimensional fractional Brownian motions, Math. Probl. Eng. 2015 (2015), Article ID 481842.
  • [18] D. Nualart, The Malliavin Calculus and Related Topics, 2nd ed., Springer, Berlin, 2010.
  • [19] E. Pardoux, S. Peng, Adapted solutions of a backward stochastic differential equation, Systems Control Lett. 14 (1990), 55-61.
  • [20] E. Pardoux, A. Ra§canu, Stochastic differential equations, Backward SDEs, Partial differential equations, Springer International Publishing, 2014.
  • [21] L.C. Young, An inequality of the Holder type connected with Stieltjes integration, Acta Math. 67 (1936), 251-282.
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-762c4c88-a74e-4008-8144-18b1962549a8
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