54
Views
6
CrossRef citations to date
0
Altmetric
Original Articles

Gradient-type noises I–partial and hybrid integrals

&
Pages 561-583 | Received 11 Jul 2008, Accepted 07 Nov 2008, Published online: 22 Sep 2010

References

  • Ayache , A , Leger , S and Pontier , M . 2002 . Drap brownien fractionnaire . Pot. Anal. , 17 : 31 – 43 .
  • Kamont , A . 1996 . On the fractional anisotropic Wiener field . Probab. Math. Stat. , 16 : 85 – 98 .
  • Xiao , Y . 2009 . “ Sample path properties of anisotropic Gaussian random fields ” . In in A minicourse on stochastic partial differential equations, Lecture Notes in Math. Vol 1962 , 145 – 212 . Berlin : Springer .
  • Walsh , JB . 1986 . “ An introduction to stochastic partial differential equations ” . In in École d'été de probabilités de Saint-Flour, XIV-1984, Lecture Notes in Math. Vol. 1180 , 265 – 439 . Berlin : Springer .
  • Dalang , RC and Frangos , NE . 1998 . The stochastic wave equation in two spatial dimensions . Ann. Probab. , 26 : 187 – 212 .
  • Lindstrøm , T . 1993 . Fractional Brownian fields as integrals of white noise . Bull. London Math. Soc. , 25 : 83 – 88 .
  • Hinz , M and Zähle , M . 2008 . Gradient type noises II–systems of stochastic partial differential equations , preprint, University of Jena .
  • Ciesielski , Z , Kerkyacharian , G and Roynette , R . 1993 . Quelques espaces fonctionnels asscciés á des processus gaussiens . Studia Math. , 107 : 171 – 204 .
  • Feyel , D and De La Pradelle , A . 1999 . Fractional integrals and Brownian processes . Pot. Anal. , 10 : 273 – 288 .
  • Lyons , TJ . 1994 . Differential equations driven by Rough signals I: An extension of an inequality by L.C. Young . Math. Res. Letters , 1 : 451 – 464 .
  • Nualart , D . 2003 . Stochastic integration with respect to fractional Brownian motion and applications . Contemp. Math. , 336 : 3 – 39 .
  • Russo , F and Vallois , P . 1993 . Forward, backward and symmetric stochastic integration . Probab. Th. Relat. Fields , 97 : 403 – 421 .
  • Young , LC . 1936 . An inequality of Hölder type, connected with Stieltjes integration . Acta Math. , 67 : 251 – 282 .
  • Zähle , M . 1998 . Integration with respect to fractal functions and stochastic calculus I . Probab. Th. and Relat. Fields , 111 : 333 – 374 .
  • Zähle , M . 2001 . Integration with respect to fractal functions and stochastic calculus II . Math. Nachr. , 225 : 145 – 183 .
  • Zähle , M . 2002 . “ Forward integrals and stochastic differential equations ” . In Seminar on Stochastic analysis, Random fields and Applications III, Progress in Probability , Edited by: Dalang , RC , Dozzi , M and Russo , F . 293 – 302 . Basel : Birkhäuser .
  • Cairoli , R and Walsh , JB . 1975 . Stochastic integrals in the plane . Acta Math. , 134 : 111 – 183 .
  • Wong , E and Zakai , M . 1974 . Martingales and stochastic integrals for processes with a multidimensional parameter . Z. Wahrsch. verw. Geb. , 29 : 109 – 122 .
  • Gowurin , M . 1936 . Über die Stieltjessche Integration abstrakter Funktionen . Fund. Math. , 27 : 255 – 268 .
  • Hille , E and Phillips , RS . 1957 . Functional Analysis and Semigroups , Providence, R.I. : AMS .
  • Samko , SG , Kilbas , AA and Marichev , OI . 1993 . Fractional Integrals and Derivatives. Theory and Applications , London : Gordon and Breach .
  • Nikolskij , SM . 1975 . Approximation of Functions of Several Variables and Embedding Theorems , New York : Springer .
  • Triebel , H . 1983 . Theory of function spaces , Basel : Geest and Portig, Leipzig, and Birkhäuser .
  • Mishura , Y . 2008 . “ Stochastic Calculus for Fractional Brownian Motion and Related Processes ” . In LNM 1929 , New York : Springer .
  • Tudor , C and Tudor , M . 2003 . On the two-parameter fractional Brownian motion and Stieltjes integrals for Hölder functions . J. Math. Anal. Appl. , 286 : 765 – 781 .
  • Erraoui , M , Nualart , D and Ouknine , Y . 2003 . Hyperbolic stochastic partial differential equations with additive fractional Brownian sheet . Stoch. Dyn. , 3 : 121 – 139 .
  • Kahane , J-P . 1985 . Some random series of functions , 2nd. ed. , Cambridge : Cambridge University Press .
  • Mandelbrot , BB and van Ness , JW . 1968 . Fractional Brownian motion, fractional Brownian noise and applications . SIAM Rev. , 10 : 422 – 437 .
  • Stein , EM . 1970 . Singular Integrals and Differentiability Properties of Functions , Princeton, NJ : Princeton University Press .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.