Stochastic analysis and local times for (N, d)-Wiener process

Peter Imkeller

Annales de l'I.H.P. Probabilités et statistiques (1984)

  • Volume: 20, Issue: 1, page 75-101
  • ISSN: 0246-0203

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Imkeller, Peter. "Stochastic analysis and local times for (N, d)-Wiener process." Annales de l'I.H.P. Probabilités et statistiques 20.1 (1984): 75-101. <http://eudml.org/doc/77225>.

@article{Imkeller1984,
author = {Imkeller, Peter},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {local times; Wong's and Zakai's calculus; Tanaka-like formulas; Burkholder's inequality; Kolmogorov's continuity criterion},
language = {eng},
number = {1},
pages = {75-101},
publisher = {Gauthier-Villars},
title = {Stochastic analysis and local times for (N, d)-Wiener process},
url = {http://eudml.org/doc/77225},
volume = {20},
year = {1984},
}

TY - JOUR
AU - Imkeller, Peter
TI - Stochastic analysis and local times for (N, d)-Wiener process
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1984
PB - Gauthier-Villars
VL - 20
IS - 1
SP - 75
EP - 101
LA - eng
KW - local times; Wong's and Zakai's calculus; Tanaka-like formulas; Burkholder's inequality; Kolmogorov's continuity criterion
UR - http://eudml.org/doc/77225
ER -

References

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  1. [1] R.J. Adler, A Hölder condition for the local time of the Brownian sheet, Indiana Univ. Math. J., t. 29, 1980, p. 793-798. Zbl0414.60076MR589443
  2. [2] J. Azema, M. Yor, Temps locaux, Astérisque, t. 52-53, Société Math. de France, Paris, 1978. MR509476
  3. [3] S.M. Berman, Gaussian processes with stationary increments: Local times and sample function properties, Ann. Math. Stat., t. 41, 1970, p. 1260-1272. Zbl0204.50501MR272035
  4. [4] P. Bernard, Quelques propriétés des trajectoires des fonctions aléatoires stables sur Rk, Ann. Inst. Henri Poincaré, t. 6 (2), 1970, p. 131-151. Zbl0196.18601MR266291
  5. [5] K. Bichteler, Stochastic integration and Lp-theory of semimartingales. Ann. Prob., t. 9, 1981, p. 49-89. Zbl0458.60057MR606798
  6. [6] R. Cairoli, J. Walsh, Stochastic integrals in the plane, Acta Mathematica, t. 134, 1975, p. 111-183. Zbl0334.60026MR420845
  7. [7] R. Cairoli, J. Walsh, Regions d'arrêt, localisations et prolongements de martingales, Z. W., t. 44, 1978, p. 279-306. Zbl0369.60043MR509203
  8. [8] W. Ehm, Sample function properties of multi-parameter stable processes, Z. W., t. 56, 1981, p. 195-228. Zbl0471.60046MR618272
  9. [9] D. Geman, J. Horowitz, Occupation densities, Ann. Prob., t. 8, 1980, p. 1-67. Zbl0499.60081MR556414
  10. [10] P. Imkeller, Ito's formula for continuous (N, d)-processes (to appear in Z. W.). Zbl0557.60040
  11. [11] P. Imkeller, Local times for a class of multi-parameter processes (to appear in Stochastics). Zbl0538.60051MR747782
  12. [12] E. Merzbach, Processus stochastiques à indices partiellement ordonnés, Rapp. interne, t. 55, École Polytechnique, 1979. 
  13. [13] C. Metraux, Quelques inégalités pour martingales à paramètre bidimensionnel. Sém. de Prob. XII, Univ. de Strasbourg, Lecture Notes in Mathematics, t. 649, p. 170-179, Springer, Berlin, 1978. Zbl0381.60042MR520006
  14. [14] P.A. Meyer, Un cours sur les intégrales stochastiques. Sém. de Prob.X, Univ. de Strasbourg, Lecture Notes in Mathematics, t. 511, Springer, Berlin, 1976. Zbl0374.60070MR501332
  15. [15] S.R. Paranjape, C. Park, Laws of the iterated logarithm of multiparameter Wiener processes, J. Multiv. Anal., t. 3, 1973, p. 132-136. Zbl0278.60053MR326852
  16. [16] L. Schwartz, Théorie des distributions, Hermann, Paris, 1966. Zbl0149.09501MR209834
  17. [17] L.T. Tran, On a problem posed by Orey and Pruitt related to the range of the N-parameter Wiener process in Rd, Z. W., t. 37, 1976, p. 27-33. Zbl0328.60043MR443063
  18. [18] S. Ustunel, Stochastic integration on nuclear spaces and its applications, Ann. Inst. Henri Poincaré, t. 18, 1982, p. 165-200. Zbl0506.60050MR662449
  19. [19] J. Walsh, The local time of the Brownian sheet, Astérisque, t. 52-53, 1978, p. 47-61. 
  20. [20] E. Wong, M. Zakai, Differentiation formulas for stochastic integrals in the plane, Stoch. Proc. Appl., t. 6, 1978, p. 339-349. Zbl0372.60078MR651571

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