On the two-parameter franctional Brownian motion and Stieltjes integrals for Hölder functions

Journal of Mathematical Analysis and Applications

Volumn 286, Issue 2, 2003, Pages 765-781

  Tudor, Constantin ^a   Tudor, Maria ^b  

^a UNIVERSITY OF BUCHAREST   (Romania)

^b BUCHAREST UNIVERSITY OF ECONOMIC STUDIES   (Romania)

Author keywords

H lder functions; Stieltjes integral; Two parameter fractional Brownian motion

Indexed keywords

EID: 0242676993     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-247X(03)00533-X     Document Type: Article

References (16)

1. A. Ayache, S. Leger, M. Pontier, Drap brownian fractionnaire, Potential Anal. 17 (2002) 31-43.
2. R.M. Dudley, R. Norvaisa, Product integrals, Young integrals and p-variation, in: Differentiability of Six Operators on Nonsmooth Functions and p-Variation, in: Lecture Notes in Math., Vol. 1703, Springer-Verlag, Berlin, 1999.
3. D. Feyel, A. De La Pradelle, On fractional Brownian processes, Potential Anal. 10 (1999) 273-288.
4. F. Klingenhöfer, Differential equations with fractal noise, Ph.D. thesis, University of Jena, 1999.
5. F. Klingenhöfer, M. Zähle, Ordinary differential equations with fractal noise, Proc. Amer. Math. Soc. 127 (1999) 1021-1028.
6. V. Kondurar, Sur l'intégrale de Stieltjes, Mat. Sb. 2 (1937) 361-366.
7. S. Leger, M. Pontier, Drap brownian fractionnaire, C. R. Acad. Sci. Paris 329 (1999) 893-898.
8. T. Lyons, Differential equations driven by rough signal. I. An extension of an inequality of L.C. Young, Math. Res. Lett. 1 (1994) 451-464.
9. T. Lyons, The interpretation and solution of ordinary differential equations driven by rough signals, in: M.C. Cranston, et al. (Eds.), Stochastic Analysis. Proceedings of the Summer Research Institute on Stochastic Analysis, Proc. Symp. Pure Math., Vol. 57, American Mathematical Society, Providence, RI, 1995, pp. 115-128.
10. D. Nualart, A. Rascanu, Differential equations driven by fractional Brownian motion, Collect. Math. 53 (2002) 55-81.
11. A.A. Ruzmaikina, Stieltjes integrals of Hölder continuous functions with applications to fractional Brownian motion, J. Stat. Phys. 1000 (2000) 1049-1069.
12. S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integrals and Derivatives, Gordon and Breach, 1993.
13. J. Yeh, Cameron-Martin translation theorems in the Wiener space of functions of two-variables, Trans. Amer. Math. Soc. 107 (1963) 409-420.
14. L.C. Young, An inequality of the Hölder type connected with Stieltjes integration, Acta Math. 67 (1936) 251-282.
15. M. Zähle, Integration with respect to fractal functions and stochastic calculus I, Probab. Theory Related Fields 111 (1998) 333-374.
16. M. Zähle, Integration with respect to fractal functions and stochastic calculus II, Math. Nachr. 225 (2001) 145-183.