On Wald's equation. Discrete time case

Leonid I. Galtchouk; Alexandre A. Novikov

Séminaire de probabilités de Strasbourg (1997)

  • Volume: 31, page 126-135

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Galtchouk, Leonid I., and Novikov, Alexandre A.. "On Wald's equation. Discrete time case." Séminaire de probabilités de Strasbourg 31 (1997): 126-135. <http://eudml.org/doc/113947>.

@article{Galtchouk1997,
author = {Galtchouk, Leonid I., Novikov, Alexandre A.},
journal = {Séminaire de probabilités de Strasbourg},
keywords = {discrete parameter martingales; Wald's equation},
language = {eng},
pages = {126-135},
publisher = {Springer - Lecture Notes in Mathematics},
title = {On Wald's equation. Discrete time case},
url = {http://eudml.org/doc/113947},
volume = {31},
year = {1997},
}

TY - JOUR
AU - Galtchouk, Leonid I.
AU - Novikov, Alexandre A.
TI - On Wald's equation. Discrete time case
JO - Séminaire de probabilités de Strasbourg
PY - 1997
PB - Springer - Lecture Notes in Mathematics
VL - 31
SP - 126
EP - 135
LA - eng
KW - discrete parameter martingales; Wald's equation
UR - http://eudml.org/doc/113947
ER -

References

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  1. Azema( J.), Gundy( R.F.), Yor( M.) (1979). Sur l'intégrabilitée uniforme des martingales continues. Séminaire de Probabilités XIV, Lecture Notes in Mathematics, 784, 53-61, Springer-Verlag, Berlin. Zbl0442.60046MR580108
  2. Burkholder ( D.L.), Gundy ( R.F.) (1970). Extrapolation and interpolation of quasilinear operators on martingales. Acta Math., 124, 249-304. Zbl0223.60021MR440695
  3. Galtchouk ( L.I.) (1980). Optional martingales. Mathematical Sbornik, 112 (154), N 4 (8), 483 - 521 (English translation :(1981) Vol.40, N4, 435-468). Zbl0449.60036MR587036
  4. Gundy ( R.F.) (1981). On a theorem of F. and M.Riesz and an equation of A.Wald. Indiana Univ.Math.Journal, 30(4), 589-605. Zbl0466.31006MR620269
  5. Feller, W. (1971). An Introduction to Probability Theory and Its Applications, vol. 2, Wiley, New York. Zbl0219.60003MR270403
  6. Kinderman ( R.P.) (1980). Asymptotic comparisons of functionals of Brownian Motion and Random Walk. Ann. Prob., 8, N6)), 1135-1147. Zbl0445.60038MR602386
  7. Klass ( M.J.) (1988). A best possible improvement of Wald's equation. Ann.prob., 16, N2, 840-853. Zbl0648.60050MR929081
  8. Liptser ( R.Sh.), Shiryaev ( A.N.) (1986). Theory of Martingales, Kluwer Academic Publ. MR1022664
  9. Meyer ( P.-A.) (1972). Martingales and Stochastic Integrals I. Lecture Notes in Mathematics, 284, Springer-Verlag. Zbl0239.60001MR426145
  10. Novikov ( A.A.) (1971). On the moment of stopping of a Wiener process. Teor. Veroythn. Primen., 16, N3, 458-465 (English translation : pp.449- 456). Zbl0258.60037MR315798
  11. Novikov ( A.A.) (1981a). A martingale approach to first passage problems and a new condition for Wald's identity. Proc.of the 3rd IFIP-WG 7/1 Working Conf.,Visegrad 1980,Lecture Notes in Control and Inf.Sci.36, 146-156. Zbl0469.60073MR653657
  12. Novikov ( A.A.) (1981b). Martingale approach to first passage problems of nonlinear boundaries. Proc.Steklov Inst.158, 130-158. Zbl0491.60038MR662841
  13. Novikov ( A.A.) (1982). On the time of crossing of a one-sided nonlinear boundary. Theor.Prob. Appl., 27, N4, 668 - 702 (English translation). Zbl0521.60055MR681458
  14. de la Pena ( V.H.) (1993). Inequalities for tails of adapted processes with an application to Wald's lemma. J. of Theoretic Prob., 6, N2, 285-302. Zbl0780.60018MR1215659
  15. Vallois ( P.) (1991). Sur la loi du maximum et du temps local d'une martingale continue uniformément intégrable. Preprint, Université de Paris VI. MR1111235
  16. Wald ( A.) (1947). Sequential Analysis, Wiley, New York; Zbl0029.15805MR20764

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