On extremal solutions of martingale problems

D. W. Stroock; M. Yor

Annales scientifiques de l'École Normale Supérieure (1980)

  • Volume: 13, Issue: 1, page 95-164
  • ISSN: 0012-9593

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Stroock, D. W., and Yor, M.. "On extremal solutions of martingale problems." Annales scientifiques de l'École Normale Supérieure 13.1 (1980): 95-164. <http://eudml.org/doc/82047>.

@article{Stroock1980,
author = {Stroock, D. W., Yor, M.},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {martingale problem; extremality; extreme points of convex sets of probability measures; local martingales},
language = {eng},
number = {1},
pages = {95-164},
publisher = {Elsevier},
title = {On extremal solutions of martingale problems},
url = {http://eudml.org/doc/82047},
volume = {13},
year = {1980},
}

TY - JOUR
AU - Stroock, D. W.
AU - Yor, M.
TI - On extremal solutions of martingale problems
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1980
PB - Elsevier
VL - 13
IS - 1
SP - 95
EP - 164
LA - eng
KW - martingale problem; extremality; extreme points of convex sets of probability measures; local martingales
UR - http://eudml.org/doc/82047
ER -

References

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  1. [1] R. DOUGLAS, On Extremal Measures and Subspace Density (Michigan Math. J., Vol. 11, 1964, pp. 644-652). Zbl0121.33102MR32 #2894
  2. [2] N. KRYLOV, The Selection of a Markov Process from a Markov System of Processes (Izv. Akad. Nauk., Vol. 38, 1973, pp. 228-248). MR49 #9945
  3. [3] P. A. MEYER, Démonstration probabiliste de certaines inégalités de Littlewood-Paley, exposé II (l'opérateur carré du champ) [Séminaire de Probabilités X (Lecture Notes in Maths, No. 511, Springer, 1976)]. Zbl0332.60032MR58 #18751a
  4. [4] D. STROOCK, Diffusion Processes Associated with Lévy Generators (Z. für Wahr., Vol. 32, 1975, pp. 209-244). Zbl0292.60122MR55 #6587
  5. [5] H. KUNITA and S. WATANABE, On Square Integrable Martingales (Nagoya Math. J., Vol. 30, 1967, pp. 209-245). Zbl0167.46602MR36 #945
  6. [6] M. CAPON, Densité des fonctions affines continues sur un convexe compact dans un espace Lp [Séminaire Choquet (Initiation à l'Analyse) 1970-1971]. 
  7. [7] J. P. ROTH, Opérateurs dissipatifs et semi-groupes dans les espaces de fonctions continues (Ann. Inst. Fourier, Vol. 26, No. 4, 1976, pp. 1-97). Zbl0331.47021MR56 #6467
  8. [8] E. B. DYNKIN, Infinitesimal Operators of Markov Processes (Th. Proba. Appl., Vol. I, 1956, pp. 34-53). Zbl0073.34901MR19,691h
  9. [9] I. GIRSANOV, An Example of Non-Uniqueness of a Solution of Ito's Stochastic Equation. (Th. Proba. App, Vol. 7, 1962, pp. 336-342). Zbl0121.35103
  10. [10] D. STROOCK and S. VARADHAN, Diffusion Processes with Boundary conditions (Comm. Pure Appl. Math, Vol. XXIV, 1971, pp. 147-225). Zbl0227.76131MR43 #2774
  11. [11] D. STROOCK and S. VARADHAN, On Degenerate Elliptic-Parabolic Operators of Second Order and their Associated Diffusions (Comm. Pure Appl. Math, Vol. XXV, 1972, pp. 651-713). Zbl0344.35041MR52 #8651
  12. [12] S. WATANABE and T. YAMADA, On the Uniqueness of Solutions of Stochastic Differential Equations (J. Math. Kyoto Univ., Vol. 11, 1971, pp. 155-167). Zbl0236.60037MR43 #4150
  13. [13] J. JACOD, A General Theorem of Representation for Martingales (Proc. of Symp. in Pure Maths., Vol. XXXI, 1977). Zbl0362.60068MR56 #1447
  14. [14] J. JACOD and M. YOR, Étude des solutions extrémales, et représentation intégrale des solutions pour certains problèmes de martingales (Z. für Wahr, Vol. 38, 1977, pp. 83-125). Zbl0346.60032MR56 #3940
  15. [15] M. YOR, Convergence de martingales dans L¹ et dans H¹ (C. R. Acad. Sc., Paris, t. 286, 1978, pp. 571-573). Zbl0382.60049MR81e:60054
  16. [16] M. YOR, Sous-espaces denses dans L¹ ou H¹, et représentation des martingales [Séminaire Strasbourg-XII (Lect. Notes in Maths, No. 649, 1978)]. Zbl0391.60046MR80m:60060
  17. [17] V. BENEŠ, Non Existence of Strong Nonanticipating Solutions to Stochastic DEs ; Implications for Functional DEs, Filtering and Control, 1977 (to appear). Zbl0367.60059
  18. [18] K. DAMBIS, On the Decomposition of Continuous Sub-Martingales (Teo. Verojatnost., Vol. 10, 1965, pp. 438-448). Zbl0141.15102MR34 #2052
  19. [19] L. DUBINS and G. SCHWARZ, On Continuous Martingales (Proc. Nat. Sc. U.S.A., Vol. 53, 1965, pp. 913-916). Zbl0203.17504MR31 #2756
  20. [20] L. DUBINS and G. SCHWARZ, On Extremal Martingale Distributions (Proc. 5th Berkeley Symp. Math. Stat. Prob., Univ. Cal. II, part I, 1967, pp. 295-299). Zbl0233.60045MR35 #7388
  21. [21] L. DUBINS, Private communication. 
  22. [22] R. GETOOR and M. SHARPE, Conformal Martingales (Invent. Math., 16, 1972, pp. 271-308). Zbl0268.60048MR46 #4603
  23. [23] I. GIRSANOV, On Transforming a Certain Class of Stochastic Processes by Absolutely continuous substitution of measures (Teo. Verojat. i Prim., Vol. 5, 1960, pp. 285-301). Zbl0100.34004MR24 #A2986
  24. [24] J. JACOD and J. MEMIN, Caractéristiques locales, et conditions de continuité absolue pour les semi-martingales (Z. für Wahr, Vol. 35, 1976, pp. 1-36). Zbl0315.60026MR54 #6264
  25. [25] N. KAZAMAKI, Changes of Time, Stochastic Integrals, and Weak Martingales (Z. für Wahr, Vol. 22, 1972, pp. 25-32). Zbl0213.19304MR46 #10064
  26. [26] H. KUNITA, Non Linear Filtering for the System with General Noise (Lect. Notes in Control Theory, Vol. 16, Springer-Verlag, 1979). Zbl0429.93060MR81g:60038
  27. [27] D. LANE, On the Fields of Some Brownian Martingales (Annals of Probability, Vol. 6, 1978, No. 3, pp. 499-508). Zbl0391.60045MR58 #3020
  28. [28] R. LIPCER and A. SHYRIAEV, Statistics of Random Processes, I. General Theory (Applications of Mathematics, vol. 5, Springer-Verlag, 1977). Zbl0364.60004
  29. [29] B. TSIREL'SON, An Example of a Stochastic Differential Equation Having no Strong Solution (Teo. Verojatnost. i Prim., Vol. 20, 1975, pp. 427-430.). Zbl0353.60061
  30. [30] E. WONG and J. VAN SCHUPPEN, Transformation of Local Martingales under a Change of Law (Ann. Probability, Vol. 2, 1974, pp. 879-888). Zbl0321.60040MR50 #11426
  31. [31] Ch. YOEURP and M. YOR, Espace orthogonal à une semi-martingale ; applications, 1977 (to appear). 
  32. [32] M. YOR, Sur l'étude des martingales continues extrémales (Stochastics, Vol. 2, 1979, pp. 191-196). Zbl0409.60043MR81c:60065
  33. [33] D. STROOCK and M. YOR, Some Remarkable Martingales, in preparation. Zbl0456.60048
  34. [34] A. ZVONKIN, A Transformation of the Phase Space of a Diffusion Process That Removes the Drift (Math. U.S.S.R. Sb., Vol. 22, 1974, pp. 129-149). Zbl0306.60049MR49 #1586
  35. [35] H. KUNITA, Absolute Continuity of Markov Processes and Extended Generators (Nagoya Math. J., Vol. 36, 1969, pp. 1-26). Zbl0186.51203MR40 #3626
  36. [36] C. DELLACHERIE and Ch. STRICKER, Changements de temps et intégrales stochastiques [Séminaire Probas, Strasbourg-XI (Lect. Notes in Maths, No. 581, Springer, 1977)]. Zbl0369.60067MR56 #16786
  37. [37] D. LEPINGLE, P. A. MEYER and M. YOR, Extrémalité et remplissage de tribus pour certaines martingales discontinues (Séminaire Probas XIV, Springer, 1980). Zbl0461.60064
  38. [38] J. AUERHAN, D. LEPINGLE and M. YOR, Construction d'une martingale réelle continue, de filtration naturelle donnée (Séminaire Probas XIV, Springer, 1980). Zbl0432.60056MR82e:60076

Citations in EuDML Documents

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  1. Jean-François Le Gall, Marc Yor, Sur l'équation stochastique de Tsirelson
  2. Daniel W. Stroock, Marc Yor, Some remarkable martingales
  3. Dominique Lépingle, Paul-André Meyer, Marc Yor, Extrémalité et remplissage de tribus pour certaines martingales purement discontinues
  4. Ljiljana Petrović, Sladjana Dimitrijević, Statistical causality and adapted distribution
  5. Martin T. Barlow, Jim Pitman, Marc Yor, On Walsh's brownian motions
  6. Walter Schachermayer, On certain probabilities equivalent to Wiener measure, d'après Dubins, Feldman, Smorodinsky and Tsirelson
  7. Jean Pellaumail, Règle maximale
  8. Michel Émery, Walter Schachermayer, A remark on Tsirelson's stochastic differential equation
  9. Jacques Azéma, Catherine Rainer, Marc Yor, Une propriété des martingales pures
  10. Samia Beghdadi-Sakrani, Une martingale non pure, dont la filtration est brownienne

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