Construction of semimartingales from pieces by the method of excursion point processes

Shinzo Watanabe

Annales de l'I.H.P. Probabilités et statistiques (1987)

  • Volume: 23, Issue: S2, page 297-320
  • ISSN: 0246-0203

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Watanabe, Shinzo. "Construction of semimartingales from pieces by the method of excursion point processes." Annales de l'I.H.P. Probabilités et statistiques 23.S2 (1987): 297-320. <http://eudml.org/doc/77311>.

@article{Watanabe1987,
author = {Watanabe, Shinzo},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {piece of Brownian motion; Poisson point process; stochastic calculus of point processes},
language = {eng},
number = {S2},
pages = {297-320},
publisher = {Gauthier-Villars},
title = {Construction of semimartingales from pieces by the method of excursion point processes},
url = {http://eudml.org/doc/77311},
volume = {23},
year = {1987},
}

TY - JOUR
AU - Watanabe, Shinzo
TI - Construction of semimartingales from pieces by the method of excursion point processes
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1987
PB - Gauthier-Villars
VL - 23
IS - S2
SP - 297
EP - 320
LA - eng
KW - piece of Brownian motion; Poisson point process; stochastic calculus of point processes
UR - http://eudml.org/doc/77311
ER -

References

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  1. [1] C. Dellacherie, Capacités et processus stochastiques, Springer, 1972. Zbl0246.60032MR448504
  2. [2] C. Dellacherie and P. Meyer, Probabilities and Potential, North-Holland, 1978. Zbl0494.60001MR521810
  3. [3] N. Ikeda and S. Watanabe, Stochastic Differential Equations and Diffusion Processes, North-Holland/Kodansha, 1981. Zbl0495.60005MR637061
  4. [4] K. Itô, Stochastic Processes, Lecture Notes Series, No. 16, Aarhus Univ., 1969. Zbl0226.60053MR260018
  5. [5] K. Itô, Kakuritsuron, Vol. III, Kiso Sūgaku Köza, Iwanami, 1978 (Japanese). 
  6. [6] K. Itô, Poisson Point Processes Attached to Markov Processes, Proc. Sixth Berkeley Sump. III, Univ. California Press, 1972, pp. 225-239. Zbl0284.60051MR402949
  7. [7] K. Itô and H.P. Mckean Jr., Diffusion Processes and Their Sample Paths, Springer, 1965. Zbl0127.09503
  8. [8] P. Lévy, Théorie de l'addition des variables aléatoires, Gauthier-Villars, 1937. Zbl0016.17003JFM63.0490.04
  9. [9] P. Lévy, Processus stochastiques et mouvement brownien, Gauthier-Villars, 1948. Zbl0034.22603MR190953
  10. [10] B. Maissonneuve, Exit Systems, Ann. Probab., Vol. 3, 1975, pp. 399-411. Zbl0311.60047MR400417
  11. [11] S. Takanobu and S. Watanabe, On the Existence and Uniqueness of Diffusion Processes with Wentzell's Boundary Conditions, Jour. Math. Kyoto Univ. (to appear). Zbl0665.60062
  12. [12] S. Watanabe, Construction of Diffusion Processes with Wentzll's Boundary Conditions by Means of Poisson Point Processes of Brownian Excursions, Probability Theory, Banach Center Publ. Vol. 5, P.W.N.-Polish Scientific Publishers, 1979, pp. 225-271. Zbl0442.60076
  13. [13] S. Watanabe, Excursion Point Processes and Diffusions, Proc. I.C.M. Warsaw, P.W.N.- Polish Scientific Publishers, 1984, pp. 255-271. Zbl0565.60044MR561485
  14. [14] D. Williams, Diffusions, Markov Processes and Martingales, Vol. 1, Foundations, John Wiley and Sons, 1979. Zbl0402.60003MR531031

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