Régularité du temps local brownien dans les espaces de Besov-Orlicz

B. Boufoussi

Studia Mathematica (1996)

  • Volume: 118, Issue: 2, page 145-156
  • ISSN: 0039-3223

Abstract

top
Let ( B t , t 0 ) be a linear Brownian motion and (L(t,x), t > 0, x ∈ ℝ) its local time. We prove that for all t > 0, the process (L(t,x), x ∈ [0,1]) belongs almost surely to the Besov-Orlicz space B M 1 , 1 / 2 with M 1 ( x ) = e | x | - 1 .

How to cite

top

Boufoussi, B.. "Régularité du temps local brownien dans les espaces de Besov-Orlicz." Studia Mathematica 118.2 (1996): 145-156. <http://eudml.org/doc/216269>.

@article{Boufoussi1996,
author = {Boufoussi, B.},
journal = {Studia Mathematica},
keywords = {local time process; Brownian motion; Besov-Orlicz space},
language = {fre},
number = {2},
pages = {145-156},
title = {Régularité du temps local brownien dans les espaces de Besov-Orlicz},
url = {http://eudml.org/doc/216269},
volume = {118},
year = {1996},
}

TY - JOUR
AU - Boufoussi, B.
TI - Régularité du temps local brownien dans les espaces de Besov-Orlicz
JO - Studia Mathematica
PY - 1996
VL - 118
IS - 2
SP - 145
EP - 156
LA - fre
KW - local time process; Brownian motion; Besov-Orlicz space
UR - http://eudml.org/doc/216269
ER -

References

top
  1. [BY] M. T. Barlow and M. Yor, Semi-martingale inequalities via the Garsia-Rodemich-Rumsey lemma, and applications to local times, J. Funct. Anal. 49 (1982), 198-229. Zbl0505.60054
  2. [Be1] S. M. Berman, Sojourns and Extremes of Stochastic Processes, Wadsworth & Brooks/Cole, Pacific Grove, 1992. 
  3. [Be2] S. M. Berman, Local times and sample function properties of stationary Gaussian processes, Trans. Amer. Math. Soc. 137 (1969), 277-299. Zbl0184.40801
  4. [Bo] A. N. Borodin, Distribution of integral functionals of Brownian motion, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 119 (1982), 19-38 (in Russian). Zbl0491.60082
  5. [BR] B. Boufoussi et B. Roynette, Le temps local brownien appartient p.s. à l’espace de Besov B p , 1 / 2 , C. R. Acad. Sci. Paris Sér. I 316 (1993), 843-848. Zbl0788.46035
  6. [C1] Z. Ciesielski, On the isomorphisms of the spaces H α and m, Bull. Acad. Polon. Sci. 8 (1960), 217-222. 
  7. [C2] Z. Ciesielski, Orlicz spaces, spline systems, and Brownian motion, Constr. Approx. 9 (1993), 191-222. Zbl0814.46022
  8. [CKR] Z. Ciesielski, G. Kerkyacharian et B. Roynette, Quelques espaces fonctionnels associés à des processus gaussiens, Studia Math. 107 (1993), 171-204. 
  9. [K1] F. B. Knight, Random walks and a sojourn density process of Brownian motion, Trans. Amer. Math. Soc. 109 (1963), 56-86. Zbl0119.14604
  10. [K2] F. B. Knight, Essentials of Brownian Motion and Diffusion, Math. Surveys 18, Amer. Math. Soc., Providence, 1981. 
  11. [KR] M. A. Krasnosel'skiĭ and Ya. B. Rutitskiĭ, Convex Functions and Orlicz Spaces, Noordhoff, Groningen, 1961. 
  12. [L] P. Lévy, Le Mouvement Brownien, Mém. Sci. Math. 126, Gauthier-Villars, Paris, 1954. 
  13. [Lu] W. A. J. Luxemburg, Banach function spaces, Thesis, Technische Hogeschool te Delft, 1955; MR 17 (1956), 285. 
  14. [M] H. P. McKean, A Hölder condition for Brownian local time, J. Math. Kyoto Univ. 1 (1962), 195-201. Zbl0121.13101
  15. [P] E. Perkins, Local time is a semi-martingale, Z. Warsch. Verw. Gebiete 60 (1982), 79-117. Zbl0468.60070
  16. [Ra] D. B. Ray, Sojourn times of diffusion processes, Illinois J. Math. 7 (1963), 615-630. Zbl0118.13403
  17. [RY] D. Revuz and M. Yor, Continuous Martingales and Brownian Motion, Springer, 1991. Zbl0731.60002
  18. [Ro] B. Roynette, Mouvement brownien et espaces de Besov, Stochastics Stochastics Rep. 43 (1993), 221-260. 
  19. [T] H. Trotter, A property of Brownian motion paths, Illinois J. Math. 2 (1958), 425-433. Zbl0117.35502
  20. [W] N. Wiener, Generalized harmonic analysis, Acta Math. 55 (130), 117-258. Zbl56.0954.02

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.