EXISTENCE AND UNIQUENESS OF STRONG SOLUTIONS TO MIXED-TYPE STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY THE FRACTIONAL BROWNIAN MOTIONS WITH HURST INDICES

Мұқаба

Дәйексөз келтіру

Толық мәтін

Ашық рұқсат Ашық рұқсат
Рұқсат жабық Рұқсат берілді
Рұқсат жабық Тек жазылушылар үшін

Аннотация

In this paper there is investigated the problem of unique solvability of the Caushy problem for the mixed type stochastic differential equation driven by the standard Brownian motion and fractional Brownian motions with Hurst indices

Авторлар туралы

M. Vaskouski

Belarusian State University

Email: vaskovskii@bsu.by
Minsk, Belarus

P. Stryuk

Belarusian State University

Email: pavel.stryouk@gmail.com
Minsk, Belarus

Әдебиет тізімі

  1. Stochastic calculus for fractional Brownian motion and applications / F. Biagini, Y. Hu, B. Oksendal, T. Zhang. — London : Springer-Verlag, 2008.
  2. Mishura, Yu.S. Stochastic calculus for fractional Brownian motion and related processes / Yu.S. Mishura. — Berlin ; Heidelberg : Springer-Verlag, 2008.
  3. Guerra, J. Stochastic differential equations driven by fractional Brownian motion and standard Brownian motion / J. Guerra, D. Nualart // Stochastic Anal. Appl. — 2008. — V. 26, № 5. — P. 1053–1075.
  4. Mishura, Y.S. Existence and uniqueness of the solution of stochastic differential equation involving Wiener process and fractional Brownian motion with Hurst index
  5. Levakov, A.A. and Vas’kovskii, M.M., Existence of weak solutions of stochastic differential equations with standard and fractional Brownian motions and with discontinuous coefficients, Differ. Equat., 2014, vol. 50, no. 2, pp. 189–202.
  6. Levakov, A.A. and Vas’kovskii, M.M., Existence of solutions of stochastic differential inclusions with standard and fractional Brownian motions, Differ. Equat., 2015, vol. 51, no. 8, pp. 991–997.
  7. Levakov, A.A. and Vas’kovskii, M.M., Properties of solutions of stochastic differential equations with standard and fractional Brownian motions, Differ. Equat., 2016, vol. 52, no. 8, pp. 972–980.
  8. Vas’kovskii, M.M., Stability and attraction of solutions of nonlinear stochastic differential equations with standard and fractional Brownian motions, Differ. Equat., 2017, vol. 53, no. 2, pp. 157–170
  9. Levakov, A.A. and Vas’kovskii, M.M., Stokhasticheskie differentsial’nye uravneniya i vklyucheniya (Stochastic Differential Equations and Inclusions), Minsk: Bel. Gos. Univ., 2019.
  10. Nualart, D. Differential equations driven by fractional Brownian motion / D. Nualart, A. Rascanu // Collectanea Mathematica. — 2002. — V. 53, № 1. — P. 55–81.
  11. Lyons, T. Differential equations driven by rough signals / T. Lyons // Revista Matematica Iberoamericana. — 1998. — V. 14, № 2. — P. 215–310.
  12. Gubinelli, M. Controlling rough paths / M. Gubinelli // J. Funct. Anal. — 2004. — V. 216, № 1. — P. 86–140.
  13. Friz, P. A Course on Rough Paths with an Introduction to Regularity Structures / P. Friz, M. Hairer. — Cham : Springer, 2014.
  14. Vaskouski, M. Asymptotic expansions of solutions of stochastic differential equations driven by multivariate fractional Brownian motions having Hurst indices greater than 1/3 / M. Vaskouski, I. Kachan // Stochastic Anal. Appl. — 2018. — V. 36, № 6. — P. 909–931.
  15. Vas’kovskii, M.M. and Karpovich, A.A., Finiteness of moments of solutions to mixed-type stochastic differential equations driven by standard and fractional Brownian motions, Differ. Equat., 2021, vol. 57, no. 2, pp. 148–154.
  16. Coutin, L. Stochastic analysis, rough path analysis and fractional Brownian motions / L. Coutin, Z. Qian // Probability Theory Related Fields. — 2002. — V. 122, № 1. — P. 108–140.
  17. Vas’kovskii, M.M., Existence and uniqueness of solutions of differential equations weakly controlled by rough paths with an arbitrary positive Holder exponent, Differ. Equat., 2021, vol. 57, no. 10, pp. 1279–1291.
  18. Vas’kovskii, M.M., Stability of solutions of stochastic differential equations weakly controlled by rough paths with arbitrary positive Holder exponent, Differ. Equat., 2021, vol. 57, no. 11, pp. 1419–1425.
  19. Vas’kovskii, M.M., Analog of the Kolmogorov equations for one-dimensional stochastic differential equations controlled by fractional Brownian motion with Hurst exponent
  20. Harang, F.A. On the theory of rough paths, fractional and multifractional Brownian motion with applications to finance : dissertation . . . master of mathematics / F.A. Harang. — Oslo, 2015. — 83 p.

Қосымша файлдар

Қосымша файлдар
Әрекет
1. JATS XML
Жүктеу

© Russian Academy of Sciences, 2024