Optimal stopping and strong approximation theorems†

References

• Berkes , I. and Philipp , W. 1979 . Approximation theorems for independent and weakly dependent random vectors . The Annals of Probability , 7 : 29 – 54 .
   Web of Science ®Google Scholar
• Billingsley , P. 1986 . Probability and Measure , New York : J. Willey .
   Google Scholar
• Dehling , H. and Philipp , W. 2002 . “ Empirical process technique for dependent data ” . In Empirical Process Technique for Dependent Data , Edited by: Dehling , H.G. , Mikosch , T. and Sorenson , M. 3 – 113 . Boston : Birkhäuser .
   Google Scholar
• Doukhan , P. 1994 . Mixing. Properties and Examples , New York : Springer-Verlag .
   Google Scholar
• Dvoretzky , A. 1970 . Asymptotic normality for sums of dependent random variables . Proc. Sixth Berekeley Symp. Math. Stat. Probab. , II : 513 – 535 .
   Google Scholar
• Heinrich , L. 1996 . Mixing properties and central limit theorem for a class of nonidentical piecewise monotonic C 2-transformations . Mathematische Nachrichten , 181 : 185 – 214 .
   Web of Science ®Google Scholar
• Ikeda , N. and Watanabe , S. 1989 . Stochastic Differential Equations and Diffusion Processes , 2nd ed. , Amsterdam : North-Holland .
   Google Scholar
• Kifer , Yu. 2000 . Game options . Finance and Stochastics , 4 : 443 – 463 .
   Google Scholar
• Kifer , Yu. 2003 . L 2 diffusion approximation for slow motion in averaging . Stoch. Dynam. , 3 : 213 – 246 .
   Google Scholar
• Kifer , Yu. 2006 . Error estimates for binomial approximations of game options . The Annals of Applied Probability , 16 : 984 – 1033 .
   Web of Science ®Google Scholar
• Komlós , J. , Major , P. and Tusnády , G. 1976 . An approximation of partial sums of independent RV's and the sample DF. II . Z. Warsch. Verw. Geb. , 34 : 33 – 56 .
   Web of Science ®Google Scholar
• Kuelbs , J. and Philipp , W. 1980 . Almost sure invariance principles for partial sums of mixing B-valued random variables . The Annals of Probability , 8 : 1003 – 1036 .
   Web of Science ®Google Scholar
• Kushner , H. 1977 . Probability Methods for Approximations in Stochastic Control and for Elliptic Equations , Academic Press .
   Google Scholar
• Lamberton , D. and Pagès , G. 1990 . Sur l'approximation of réduites . Ann. l'Inst. H.Poincaré , 26 : 331 – 355 .
   Google Scholar
• Lepeltier , J.P. and Maingueneau , J.P. 1984 . Le jeu de Dynkin en theorie generale sans l'hypothese de Mokobodski . Stochastics , 13 : 24 – 44 .
   Google Scholar
• Mulinacci , S. and Pratelli , M. 1998 . Functional convergence of Snell envelopes: applications to American options approximations . Finance and Stochastics , 2 : 311 – 327 .
   Google Scholar
• Ohtsubo , Y. 1986 . Optimal stopping in sequential games with or without a constraint of always terminating . Mathematics of Operations Research , 11 : 591 – 607 .
   Web of Science ®Google Scholar
• Peligrad , M. 1982 . Invariance principles for mixing sequences of random variables . The Annals of Probability , 10 : 968 – 981 .
   Web of Science ®Google Scholar
• Petrov , V.V. 1995 . Limit Theorems of Probability Theory. Sequences of Independent Random Variables , Oxford : Oxford University Press .
   Google Scholar
• Rudin , W. 1987 . Real and Complex Analysis , New York : McGraw-Hill .
   Google Scholar
• Shiryaev , A.N. 1984 . Probability , New York : Springer-Verlag .
   Google Scholar
• Strassen , V. 1967 . Almost sure behavior of sums of independent random variables and martingales . Proc. Fifth Berkeley Symp. Math. Stat. Probab. , II : 315 – 343 . Part 1,
   Google Scholar
• Yokoyama , R. 1980 . Moment bounds for stationary mixing sequences . Z. Wahrsch. Verw. Gebiete , 52 : 45 – 57 .
   Web of Science ®Google Scholar
• Zaitsev , A.Yu. 2000 . Multidimensional version of a result of Sakhanenko in the invariance principle for vectors with finite exponential moments, I–III . Theory Probab. Appl. , 45 : 624 – 641 . 45 (2001), 490–514, 676–698
   Web of Science ®Google Scholar