Fetching the paper…
Reading the bibliography…
We give concentration bounds for martingales that are uniform over finite times and extend classical Hoeffding and Bernstein inequalities.
[author] Khinchin, A. Ya.A. Y. (1924). Über einen Satz der Wahrscheinlichkeitsrechnung. Fundamenta Mathematicae 6 9–20
1924
Earlier work this paper cites.
[author] Erdős, PaulP. (1942). On the law of the iterated logarithm. Annals of Mathematics 419–436. 2722836
1942
Earlier work this paper cites.
[author] Feller, WilliamW. (1943). The general form of the so-called law of the iterated logarithm. Transactions of the American Mathematical Society 54 373–402. 0009263
1943
Earlier work this paper cites.
[author] Darling, D. A.D. A. and Erdös, P.P. (1956). A limit theorem for the maximum of normalized sums of independent random variables. Duke Math. J. 23 143–155. 0074712
1956
Earlier work this paper cites.
[author] Hoeffding, WassilyW. (1963). Probability inequalities for sums of bounded random variables. J. Amer. Statist. Assoc. 58 13–30. 0144363
1963
Earlier work this paper cites.
[author] Darling, D. A.D. A. and Robbins, HerbertH. (1967). Iterated logarithm inequalities. Proc. Nat. Acad. Sci. U.S.A. 57 1188–1192. 0211441
1967
Earlier work this paper cites.
[author] Robbins, HerbertH. (1970). Statistical methods related to the law of the iterated logarithm. Ann. Math. Statist. 41 1397–1409. 0277063
1970
Earlier work this paper cites.
[author] Robbins, HerbertH. and Siegmund, DavidD. (1970). Boundary crossing probabilities for the Wiener process and sample sums. Ann. Math. Statist. 41 1410–1429. 0277059
1970
Cited alongside, same era.
[author] Stout, William F.W. F. (1970). A martingale analogue of Kolmogorov’s law of the iterated logarithm. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 15 279–290. 0293701
1970
Cited alongside, same era.
[author] Heyde, C. C.C. C. (1972). Martingales: a case for a place in the statistician’s repertoire. Austral. J. Statist. 14 1–9. 0383473
1972
Cited alongside, same era.
[author] Freedman, David A.D. A. (1975). On tail probabilities for martingales. Ann. Probability 3 100–118. 0380971
1975
Cited alongside, same era.
[author] Shafer, GlennG. and Vovk, VladimirV. (2001). Probability and finance. Wiley Series in Probability and Statistics. Financial Engineering Section. Wiley-Interscience, New York It’s only a game! 10.1002/0471249696 1852450
[author] Talagrand, MichelM. (2005). The generic chaining. Springer Monographs in Mathematics. Springer-Verlag, Berlin Upper and lower bounds of stochastic processes. 2133757
2005
Later among the works it cites.
[author] de la Peña, Victor H.V. H., Klass, Michael J.M. J. and Lai, Tze LeungT. L. (2007). Pseudo-maximization and self-normalized processes. Probability Surveys 4 172-192. 2368950
2007
Later among the works it cites.
Peres, Y
2009
Later among the works it cites.
[author] Durrett, RickR. (2010). Probability: theory and examples, fourth ed. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, Cambridge. 10.1017/CBO9780511779398 2722836
2010
Later among the works it cites.
[author] Boucheron, StéphaneS., Lugosi, GáborG. and Massart, PascalP. (2013). Concentration inequalities: A nonasymptotic theory of independence. Oxford University Press, Oxford. 10.1093/acprof:oso/9780199535255.001.0001 3185193
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2001
Cited alongside, same era.
[author] Rogers, L. C. G.L. C. G. (2002). Monte Carlo valuation of American options. Math. Finance 12 271–286. 10.1111/1467-9965.02010 1910596
2002
Cited alongside, same era.
[author] Haugh, Martin B.M. B. and Kogan, LeonidL. (2004). Pricing American options: a duality approach. Oper. Res. 52 258–270. 10.1287/opre.1030.0070 2066400
2004
Cited alongside, same era.
2013
Later among the works it cites.
Jamieson, K. G
2014
Closest in time.