Inequalities for a pair of processes stopped at a random time

Proceedings of the London Mathematical Society

Volumn s3-52, Issue 1, 1986, Pages 142-172

  Barlow, M T ^a   Jacka, S D ^b   Yor, M ^c  

^a Statistical Laboratory   (United Kingdom)

^b UNIVERSITY OF WARWICK   (United Kingdom)

^c University of Paris VII LPSM partially supported by ERC Starting Grant 680275 MALIG   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84963019945     PISSN: 00246115     EISSN: 1460244X     Source Type: Journal    
DOI: 10.1112/plms/s3-52.1.142     Document Type: Article

References (21)

1. J. M. BISMUT and M. YOR, ‘An inequality for processes which satisfy Kolmogorov’s continuity criterion. Application to continuous martingales’, J. Fund. Anal., 51 (1983), 166-173.
2. D. BURKHOLDER, ‘Distribution function inequalities for martingales’, Ann. Probab., 1 (1973), 19-42.
3. R. CAIROLI and J. B. WALSH, ‘Stochastic integrals in the plane’, Acta Math., 134 (1975), 111-183.
4. J. Y. CALAIS and M. GÉNIN, ‘Sur les martingales locales continues indexées par [0, ∞ [', Séminaire Probabilité XVII, Lecture Notes in Mathematics 986 (Springer, Berlin, 1983), pp. 162-178.
5. C. DELLACHERIE, Capacites et processus stochastiques (Springer, Berlin, 1972).
6. C. DELLACHERIE and P. A. MEYER, Probabilités et potentiel, Vol. II (Hermann, Paris, 1980).
7. X. FERNIQUE, ‘Régularité des trajectoires des fonctions aleatoires gaussiennes’, École d'Été de Probabilites de Saint-Flour IV, Lecture Notes in Mathematics 480 (Springer, Berlin, 1975).
8. D. FREEDMAN, ‘On tail probabilities for martingales’, Ann. Probab., 3 (1975), 100-118.
9. N. IKEDA and S. WATANABE, Stochastic differential equations and diffusion processes (NorthHolland/Kodansha, Amsterdam, 1981).
10. M. A. KRASNOSELSKI and Y. B. RUTICKI, Convex functions and Orlicz spaces (translated from Russian, Noordhoff, Groningen, 1961).
11. E. LENGLART, D. LÉPINGLE, and M. PRATELLI, ‘Présentation unifiee de certaines inégalités de la théoriedes martingales’, Séminaire Probabilité XIV, Lecture Notes in Mathematics 784 (Springer, Berlin, 1982), pp. 26-48.
12. M. Métivier and J. Pellaumail, ‘Une formule de majoration pour martingales’, C. R. Acad. Sci. Paris Sér. A, 215 (1977), 685-688.
13. P. A. Meyer, Martingales and stochastic integrals, Lecture Notes in Mathematics 284 (Springer, Berlin, 1972).
14. J. Neveu, Discrete parameter martingales (North Holland, Amsterdam, 1975).
15. H. ROBBINS and D. SIEGMUND, ‘Boundary crossing probabilities for the Wiener process and samplesums’, Ann. Math. Statist., 41 (1970), 1410-1429.
16. W. F. STOUT, ‘Maximal inequalities and the law of the iterated logarithm’, Ann. Probab., 1 (1973),322-328.
17. W. F. STOUT, ‘A martingale analogue of Kolmogorov’s law of the iterated logarithm’, Z. Wahrsch. Verw. Gebiete, 15 (1970), 279-290.
18. J. O. STRÖMBERG, ‘Bounded mean oscillation with Orlicz norms and duality of Hardy spaces’, IndianaUniv. Math. J., 28 (1979), 511-544.
19. Ch. YOEURP, ‘Décompositions des martingales locales et formules exponentielles’, Séminaire Probabilité X, Lecture Notes in Mathematics 511 (Springer, Berlin, 1976), pp. 501-504.
20. M. YOR, ‘Une inégalité optimale pour le mouvement Brownien arrêté à un temps quelconque’, C. R.Acad. Sci. Paris Ser. A, 296 (1983), 407-409.
21. M. YOR, ‘Inegalites de martingales continues arretees a un temps quelconque: I, théorèmes généraux’, preprint, Université Paris VI, 1983.