A counterexample for the Markov property of local time for diffusions on graphs

Nathalie Eisenbaum; Haya Kaspi

Séminaire de probabilités de Strasbourg (1995)

  • Volume: 29, page 260-265

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Eisenbaum, Nathalie, and Kaspi, Haya. "A counterexample for the Markov property of local time for diffusions on graphs." Séminaire de probabilités de Strasbourg 29 (1995): 260-265. <http://eudml.org/doc/113910>.

@article{Eisenbaum1995,
author = {Eisenbaum, Nathalie, Kaspi, Haya},
journal = {Séminaire de probabilités de Strasbourg},
keywords = {Markov property; local time; conditionally independent; Brownian motion},
language = {eng},
pages = {260-265},
publisher = {Springer - Lecture Notes in Mathematics},
title = {A counterexample for the Markov property of local time for diffusions on graphs},
url = {http://eudml.org/doc/113910},
volume = {29},
year = {1995},
}

TY - JOUR
AU - Eisenbaum, Nathalie
AU - Kaspi, Haya
TI - A counterexample for the Markov property of local time for diffusions on graphs
JO - Séminaire de probabilités de Strasbourg
PY - 1995
PB - Springer - Lecture Notes in Mathematics
VL - 29
SP - 260
EP - 265
LA - eng
KW - Markov property; local time; conditionally independent; Brownian motion
UR - http://eudml.org/doc/113910
ER -

References

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  1. [A] Atkinson, B. (1983). "On Dynkin's Markov property of random fields associated with symmetric processes". Stoch. Proc. Appl.15, 193-201. Zbl0526.60048MR702491
  2. [D] Dynkin, E.B. (1984). "Local times and quantum fields". Sem. on Stoch. Proc., 1983, Birkhauser, 69-84. Zbl0554.60058MR902412
  3. [E] Eisenbaum, N. (1994). "Dynkin's isomorphism theorem and the Ray-Knight theorems". Probability Theory and Related Fields99, No. 2, 321-335. Zbl0801.60064MR1278888
  4. [EK] Eisenbaum, N. and Kaspi, H. (1993). "A necessary and sufficient condition for the Markov property of the local time process". Ann. of Probab.21, No. 3, 1591-1598. Zbl0788.60091MR1235430
  5. [K] Knight, F.B. (1963). "Random walks and a sojourn density process of Brownian motion". Trans. Amer. Math. Soc.109, 56-86. Zbl0119.14604MR154337
  6. [L] Leuridan, C. "Problèmes liés aux temps locaux du mouvement Brownien: Estimation de norme Hp, théorèmes de Ray-Knight sur le tore, point le plus visité". Thèse de doctorat de mathématiques de l'Université Joseph Fourier. 
  7. [R] Ray, D.B. (1963). "Sojourn time of a diffusion process". Ill. J. Maths.7, 615-630. Zbl0118.13403MR156383
  8. [S] Sheppard, P. (1985). "On the Ray-Knight property of local times". J. London Math. Soc.31, 377-384. Zbl0535.60070MR809960
  9. [W] Walsh, J.B. (1978). "Excursions and local time". Temps Locaux, Asterisque 52-53, 159-192. MR509476

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