The existence of a multiple spider martingale in the natural filtration of a certain diffusion in the plane
Séminaire de probabilités, Tome 33 (1999), pp. 277-290 
@article{SPS_1999__33__277_0,
     author = {Watanabe, Shinzo},
     title = {The existence of a multiple spider martingale in the natural filtration of a certain diffusion in the plane},
     journal = {S\'eminaire de probabilit\'es},
     pages = {277--290},
     year = {1999},
     publisher = {Springer - Lecture Notes in Mathematics},
     volume = {33},
     mrnumber = {1768001},
     zbl = {0953.60069},
     language = {en},
     url = {https://www.numdam.org/item/SPS_1999__33__277_0/}
}
TY  - JOUR
AU  - Watanabe, Shinzo
TI  - The existence of a multiple spider martingale in the natural filtration of a certain diffusion in the plane
JO  - Séminaire de probabilités
PY  - 1999
SP  - 277
EP  - 290
VL  - 33
PB  - Springer - Lecture Notes in Mathematics
UR  - https://www.numdam.org/item/SPS_1999__33__277_0/
LA  - en
ID  - SPS_1999__33__277_0
ER  - 
%0 Journal Article
%A Watanabe, Shinzo
%T The existence of a multiple spider martingale in the natural filtration of a certain diffusion in the plane
%J Séminaire de probabilités
%D 1999
%P 277-290
%V 33
%I Springer - Lecture Notes in Mathematics
%U https://www.numdam.org/item/SPS_1999__33__277_0/
%G en
%F SPS_1999__33__277_0
Watanabe, Shinzo. The existence of a multiple spider martingale in the natural filtration of a certain diffusion in the plane. Séminaire de probabilités, Tome 33 (1999), pp. 277-290. https://www.numdam.org/item/SPS_1999__33__277_0/

[BEKSY] M.T. Barlow, M. Émery F.B. Knight, S. Song et M. Yor, Autour d'un théorème de Tsirelson sur des filtrations browniennes et non browniennes, Séminaire de Probabilités XXXII, LNM 1686, Springer, Berlin (1998), 264-305 | Zbl | MR | Numdam

[BPY] M.T. Barlow, J.W. Pitman and M. Yor, On Walsh's Brownian motions, Séminaire de Probabilités XXIII, LNM 1372, Springer, Berlin (1989), 275-293 | Zbl | MR | Numdam

[DV] M.H. Davis and P. Varaiya, The multiplicity of an increasing family of σ-fields, Annals of Probab., 2(1974), 958-963 | Zbl | MR

[DFST] L. Dubins, J. Feldman, M. Smorodinsky and B. Tsirelson, Decreasing sequences of σ-fields and a measure change for Brownian motion, Annals of Probab., 24(1996), 882-904 | Zbl | MR

[EY] M. Émery et M. Yor, Sur un théorème de Tsirelson relatif à des mouvements browniens corrélés et à la nullité de certains temps locaux, Séminaire de Probabilités XXXII, LNM 1686, Springer, Berlin (1998), 306-312 | Zbl | MR | Numdam

[FOT] M. Fukushima, Y. Oshima and M. Takeda, Dirichlet Forms and Symmetric Markov Processes, Walter de Gruyter, Berlin-New York, 1994 | Zbl | MR

[H] T. Hida, Canonical representation of Gaussian processes and their applications, Mem. Colleg. Sci. Univ. Kyoto, A, 33(1960), 109-155 | Zbl | MR

[IW 1] N. Ikeda and S. Watanabe, The Local Structure of Diffusion Processes, (Kakusan-Katei no Kyokusho Kôzô), Seminar on Probab. Vol. 35, Kakuritsuron Seminar, 1971 (in Japanese) | MR

[IW 2] N. Ikeda and S. Watanabe, The local structure of a class of diffusions and related problems, Proc. 2nd. Japan-USSR Symp, LNM 330, Springer, Berlin (1973), 124-169 | Zbl | MR

[IW 3] N. Ikeda and S. Watanabe, Stochastic Differential Equations and Diffusion Processes, Second Edition, North-Holland/Kodansha, Amsterdam/Tokyo, 1988 | Zbl | MR

[I] K. Itô, Poisson point processes attached to Markov processes, in Kiyosi Itô, Selected Papers, Springer, New York (1987), 543-557, Originally published in Proc. Sixth Berkeley Symp. Math. Statist. Prob. III(1970), 225-239 | Zbl | MR

[KW] H. Kunita and S. Watanabe, On square integrable martingales, Nagoya Math Jour. 30(1967), 209-245 | Zbl | MR

[MW] M. Motoo and S. Watanabe, On a class of additive functionals of Markov processes, J. Math. Kyoto Univ. 4(1965), 429-469 | Zbl | MR

[N] M. Nisio, Remark on the canonical representation of strictly stationary processes, J. Math. Kyoto Univ. 1(1961), 129-146 | Zbl | MR

[RY] D. Revuz and M. Yor, Continuous Martingales and Brownian Motion, Springer, Berlin, 1991 | Zbl | MR

[S] A.B. Skorokhod, Random processes in infinite dimensional spaces, Proc. ICM. 1986, Berkeley, Amer. Math. Soc., 163-171 (in Russian). | Zbl

[T] B. Tsirelson, Triple points: From non-Brownian filtrations to harmonic measures, Geom. Func. Anal. 7(1997), 1096-1142 | Zbl | MR

[War] J. Warren, On the joining of sticky Brownian motion, in this volume. | Zbl | Numdam

[Wat] S. Watanabe, Construction of semimartingales from pieces by the method of excursion point processes, Ann. Inst. Henri Poincaré 23(1987), 293-320 | Zbl | MR | Numdam

[We] M. Weil, Quasi-processus, Séminaire de Probabilités IV, LNM 124, Springer, Berlin (1970), 216-239 | Zbl | MR | Numdam

[Y] M. Yor, Some Aspects of Brownian Motion, Part II, Lectures in Math. ETH Zürich, Birkhauser, 1997 | Zbl | MR