Strong existence, uniqueness and non-uniqueness in an equation involving local time

Martin T. Barlow; Edwin A. Perkins

Séminaire de probabilités de Strasbourg (1983)

  • Volume: 17, page 32-61

How to cite

top

Barlow, Martin T., and Perkins, Edwin A.. "Strong existence, uniqueness and non-uniqueness in an equation involving local time." Séminaire de probabilités de Strasbourg 17 (1983): 32-61. <http://eudml.org/doc/113450>.

@article{Barlow1983,
author = {Barlow, Martin T., Perkins, Edwin A.},
journal = {Séminaire de probabilités de Strasbourg},
keywords = {local time},
language = {eng},
pages = {32-61},
publisher = {Springer - Lecture Notes in Mathematics},
title = {Strong existence, uniqueness and non-uniqueness in an equation involving local time},
url = {http://eudml.org/doc/113450},
volume = {17},
year = {1983},
}

TY - JOUR
AU - Barlow, Martin T.
AU - Perkins, Edwin A.
TI - Strong existence, uniqueness and non-uniqueness in an equation involving local time
JO - Séminaire de probabilités de Strasbourg
PY - 1983
PB - Springer - Lecture Notes in Mathematics
VL - 17
SP - 32
EP - 61
LA - eng
KW - local time
UR - http://eudml.org/doc/113450
ER -

References

top
  1. 1. N. El Karoui, M. Chaleyat-Maurel. Un problème de réflexion et ses applications au temps local et aux equations différentielles stochastiques sur R. Cas continu. In: Temps Locaux-Astérisque52-53, 117-144 (1978). 
  2. 2. N. El KarouiSur les montées des semi-martingales. In: Temps Locaux-Astérisque52-53, 63-72 (1978). 
  3. 3. M. Emery, E. Perkins. La Filtration de B+L. Z. Wahrscheinlichkeitstheorie verw. Geb.59, 383-390 (1982). Zbl0466.60073MR721634
  4. 4. J.M. Harrison, L.A. Shepp. On skew Brownian motion. Ann. of Probability9, 309-313 (1981). Zbl0462.60076MR606993
  5. 5. D. Hoover, E. Perkins. Nonstandard construction of the stochastic integral and applications to stochastic differential equations I, II. (To appear in Trans. Amer. Math. Soc.). Zbl0533.60063MR678335
  6. 6. K. Ito. Poisson point processes attached to Markov processes. Proc. 6th Berk. Symp. Math. Statist. Prob., 225-239 (1970). Zbl0284.60051MR402949
  7. 7. J. Jacod, J. Memin. Weak and strong solutions of stochastic differential equations: existence and uniqueness. In Stochastic Integrals, Lect. Notes. Math.851, Springer (1981). Zbl0471.60066MR620991
  8. 8. H.J. Keisler. An infinitesimal approach to stochastic analysis. (To appear as an A.M.S. Memoir). Zbl0529.60062MR732752
  9. 9. S. Kosciuk. Stochastic solutions to partial differential equations. Ph.D. thesis, U. of Wisconsin (1982). Zbl0521.60073MR698955
  10. 10. J.-F. LeGall. Temps locaux et equations différentielles stochastiques. Thèse de troisième cycle, Paris VI (1982). 
  11. 11. P.A. Loeb. An introduction to nonstandard analysis and hyperfinite probability theory. In: Probabilistic Analysis and Related Topics Vol. 2, 105-142, New York : Academic Press (1979). Zbl0441.03027MR556680
  12. 12. P. Protter, A.-S. Sznitman. An equation involving local time. Sem. Prob. XVII. Lect. Notes Math.986, Springer Zbl0509.60078MR770395
  13. 13. T. Yamada, S. Watanabe. On the uniqueness of solutions of stochastic differential equations I. J. Math. Kyoto Univ.II, 155-167 (1971). Zbl0236.60037MR278420
  14. 14. M. Yor. Sur la continuité des temps locaux associés à certaines semi-martingales. In: Temps Locaux-Astérisque52-53, 23-35 (1978). 
  15. 15. A. Dvoreksky, P. Erdos, S. Kakutani. Non-increasing everywhere of the Brownian motion process. Proc. 4th Berk. Sympl Math. Statist. Prob.II, 103-116 (1961). Zbl0111.15002
  16. 16. J.W. Pitman. One dimensional Brownian motion and the three-dimensional Bessel process. Adv. Appl. Prob.7, 511-526 (1975). Zbl0332.60055MR375485

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.