Probability structure preserving and absolute continuity

Yaozhong Hu

Annales de l'I.H.P. Probabilités et statistiques (2002)

  • Volume: 38, Issue: 4, page 557-580
  • ISSN: 0246-0203

How to cite

top

Hu, Yaozhong. "Probability structure preserving and absolute continuity." Annales de l'I.H.P. Probabilités et statistiques 38.4 (2002): 557-580. <http://eudml.org/doc/77725>.

@article{Hu2002,
author = {Hu, Yaozhong},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {stochastic integral; probability structure preserving mapping; absolute continuity; fractional Brownian motion; Radon-Nikodym derivative; anticipative Girsanov theorem},
language = {eng},
number = {4},
pages = {557-580},
publisher = {Elsevier},
title = {Probability structure preserving and absolute continuity},
url = {http://eudml.org/doc/77725},
volume = {38},
year = {2002},
}

TY - JOUR
AU - Hu, Yaozhong
TI - Probability structure preserving and absolute continuity
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2002
PB - Elsevier
VL - 38
IS - 4
SP - 557
EP - 580
LA - eng
KW - stochastic integral; probability structure preserving mapping; absolute continuity; fractional Brownian motion; Radon-Nikodym derivative; anticipative Girsanov theorem
UR - http://eudml.org/doc/77725
ER -

References

top
  1. [1] E. Alòs, O. Mazet,, D. Nualart, Stochastic calculus with respect to fractional Brownian motion with Hurst parameter lesser than 1/2, Stochastic Process. Appl.86 (2000) 121-139. Zbl1028.60047MR1741199
  2. [2] R. Buckdahn, Anticipative Girsanov transformations and Skorohod stochastic differential equations, Mem. Amer. Math. Soc.111 (533) (1994). Zbl0849.60053MR1219706
  3. [3] W. Dai, C.C. Heyde, Itô formula with respect to fractional Brownian motion and its application, J. Appl. Math. Stoch. Anal.9 (1996) 439-448. Zbl0867.60029MR1429266
  4. [4] L. Decreusefond, A.S. Üstünel, Stochastic analysis of the fractional Brownian motion, Potential Analysis10 (1999) 177-214. Zbl0924.60034MR1677455
  5. [5] T.E. Duncan, Y.Z. Hu, B. Pasik-Duncan, Stochastic calculus for fractional Brownian motion, I. Theory, SIAM J. Control Optim.38 (2000) 582-612. Zbl0947.60061MR1741154
  6. [6] Y.Z. Hu, G. Kallianpur, Exponential integrability and application to stochastic quantization, Appl. Math. Optim.37 (1998) 295-353. Zbl0903.60046MR1610803
  7. [7] Y.Z. Hu, P.A. Meyer, Chaos de Wiener et intégrale de Feynman, in: Séminaire de Probabilités, XXII, Lecture Notes in Math., 1321, Springer, Berlin, 1988, pp. 51-71. Zbl0644.60081MR960508
  8. [8] Y.Z. Hu, P.A. Meyer, Sur les intégrales multiples de Stratonovich, in: Séminaire de Probabilités, XXII, Lecture Notes in Math., 1321, Springer, Berlin, 1988, pp. 72-81. Zbl0644.60082MR960509
  9. [9] Y.Z. Hu, P.A. Meyer, On the approximation of multiple Stratonovich integrals, in: Stochastic Processes, Springer, New York, 1993, pp. 141-147. Zbl0798.60057MR1427310
  10. [10] Y.Z. Hu, B. Øksendal, Fractional white noise calculus and applications to finance, Preprint, University of Oslo, 1999. Zbl1045.60072
  11. [11] Y.Z. Hu, Prediction and translation of fractional Brownian motions, in: Hida T., (Eds.), Stochastics in Finite and Infinite Dimensions, Birkhäuser, 2000, pp. 153-171. Zbl0973.60059MR1797086
  12. [12] S. Janson, Gaussian Hilbert Spaces, Cambridge University Press, 1997. Zbl0887.60009MR1474726
  13. [13] P. Malliavin, Stochastic Analysis, Grundlehren der Mathematischen Wissenschaften, 313, Springer, Berlin, 1997. Zbl0878.60001MR1450093
  14. [14] B.B. Mandelbrot, J.W. Van Ness, Fractional Brownian motions, fractional noises and applications, SIAM Rev.10 (1968) 422-437. Zbl0179.47801MR242239
  15. [15] D. Nualart, The Malliavin Calculus and Related Topics, Probability and its Applications, Springer, New York, 1995. Zbl0837.60050MR1344217
  16. [16] J. Neveu, Processus aléatoires gaussiens, Les Presses de l'Université de Montréal, Montreal, Quebec, 1968. Zbl0192.54701MR272042
  17. [17] J. Norris, Simplified Malliavin calculus, in: Séminaire de Probabilités, XX, 1984/85, Lecture Notes in Math., 1204, Springer, Berlin, 1986, pp. 101-130. Zbl0609.60066MR942019
  18. [18] V. Pipiras, M.S. Taqqu, Integration questions related to fractional Brownian motion, Probab. Theory Related Fields118 (2000) 251-291. Zbl0970.60058MR1790083
  19. [19] S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach Science Publishers, 1993. Zbl0818.26003MR1347689
  20. [20] D.W. Stroock, S.R.S. Varadhan, Multidimensional Diffusion Processes, Springer, Berlin, 1979. Zbl0426.60069MR532498
  21. [21] A.S. Üstünel, M. Zakai, Transformation of Measure on Wiener Space, Springer Monographs in Mathematics, Springer, Berlin, 2000. Zbl0938.46045MR1736980

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.