본문 바로가기
KERD
논문KCI 등재

The law of a stochastic integral with two independent bifractional Brownian motions

Junfeng Liu
대한수학회 (The Korean Mathematical Society)|2011.10|대한수학회논문집 (Communications of the KMS)|제26권 제4호|pp. 669-684

1

조회

0

다운로드

0

인용

0

참고문헌

키워드

characteristic functionstochastic integralbifractional Brownian motion
주제분류수학

초록

In this note, we obtain the expression of the characteristic fucntion of the random variable (기호) , where B^(α, β) and B^(H,K) are two independent bifractional Brownian motions with indices α ∈ (0, 1), β ∈ (0, 1] and HK ∈ ( 1/2, 1), respectively.

Abstract

In this note, we obtain the expression of the characteristic fucntion of the random variable (기호) , where B^(α, β) and B^(H,K) are two independent bifractional Brownian motions with indices α ∈ (0, 1), β ∈ (0, 1] and HK ∈ ( 1/2, 1), respectively.

참고문헌 (19)

  1. E. Alos, "Stochastic calculus with respect to Gaussian pro- cesses", Ann. Probab, 29(2), pp.766~801 (2001)
  2. X. Bardina, "The law of a stochastic integral with two independent fractional Brownian motions", Bol. Soc. Mat. Mexicana, 13(1), pp.231~242 (2007)
  3. R. Berthuet, "Loi du logharitme itere pour cetaines integrales stochastiques", Ann. Sci. Univ. Clermont-Ferrand Math, 69, pp.9~18 (1981)
  4. F. Biagini, "Stochastic Calculus for Fractional Brow- nian Motion and Applications" (2008), Springer-Verlag London, Ltd
  5. P. Caithamer, "Decoupled double stochastic fractional integrals", Stochastics, 77(3), pp.205~210 (2005)
  6. K. Es-Sebaiy, "Multidimensional bifractional Brownian motion: It^o and Tanaka formulas", Stoch. Dyn, 7(3), pp.365~388 (2007)
  7. C. Houdre, "An example of innite dimensional quasi-helix", Contemp. Math, 336, pp.195~201 (2003)
  8. Y. Hu, "Integral transformations and anticipative calculus for fractional Brownian mo- tions", Mem. Amer. Math. Soc, 175(825), pp.viii+127~ (2005)
  9. R. Klein, "On quadratic variation of processes with Gaussian increments", Ann. Probab, 3(4), pp.716~721 (1975)
  10. I. Kruk, "Wiener integrals, Malliavin calculus and covariance measure structure", J. Funct. Anal, 249(1), pp.92~142 (2007)
  11. P. Lei, "A decomposition of the bifractional Brownian motion and some applications", Statist. Probab. Lett, 79(5), pp.619~624 (2009)
  12. P. Levy, "Wiener's random function, and other Laplacian random functions, Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, 1950", pp.171~187 (1951), University of California Press
  13. Y. Mishura, "Stochastic Calculus for Fractional Brownian Motion and Related Processes, Lecture Notes in Mathematics, 1929" (2008), Springer-Verlag
  14. D. Nualart, "Malliavin Calculus and Related Topics" (2006), Springer
  15. P. E. Protter, "Stochastic Integration and Differential Equations" (2005), Springer-Verlag
  16. F. Russo, "On bifractional Brownian motion", Stochastic Process. Appl, 116(5), pp.830~856 (2006)
  17. C. A. Tudor, "Sample path properties of bifractional Brownian motion", Bernoulli, 13(4), pp.1023~1052 (2007)
  18. L. Yan, "Quadratic covariation and It^o formula for a bifractional Brownian motion" (2008), preprint
  19. M. Yor, "Remarques sur une formule de Paul Levy", Lecture Notes in Math, 784, pp.343~346 (1980)

관련 논문AI추천

WEAK CONVERGENCE FOR MULTIPLE STOCHASTIC INTEGRALS IN SKOROHOD SPACE김윤태강원경기수학회 · 한국수학논문집2014 · 제22권 제1호Operator fractional Brownian sheet and martingale differencesGuangjun Shen, Hongshuai Dai, Liangwen Xia대한수학회 · 대한수학회보2018 · 제55권 제1호Stochastic differential equations driven by an additive fractional Brownian sheetOussama El Barrimi, Youssef Ouknine대한수학회 · 대한수학회보2019 · 제56권 제2호The local time of the linear self-attracting diffusion driven by weighted fractional Brownian motionGuangjun Shen, Qin Chen, Qingbo Wang대한수학회 · 대한수학회보2020 · 제57권 제3호A note on functional limit theorem for the increments of FBM in sup-norm황교신영남수학회 · East Asian Mathematical Journal2008 · 제24권 제3호Chung-type law of the iterated logarithm of l^∞-valued Gaussian processesWensheng Wang, Yong-Kab Choi, Zhenyan Lin대한수학회 · 대한수학회지2009 · 제46권 제2호

이 간행물의 다른 논문 (16건)

Bipolar fuzzy a-ideals of BCI-algebras전영배, 이경자pp. 531-542Free algebras over a poset in varietiesAldo Figallo, Jr., Alicia Zilianipp. 543-549A short proof of an identity for cubic partition functionXinhua Xiongpp. 551-555Quasi-Armendariz property for skew polynomial ringsMuhittin Ba(특수문자)er, 곽태근pp. 557-573On the convergence of a Newton-like method under weak conditionsIoannis K. Argyros, Hongmin Renpp. 575-584
원문 보기