Large deviations for martingales and derivatives |
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| Authors: | S Butler S Pavlov |
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| Institution: | a Department of Mathematics, University of Illinois at Urbana-Champaign, 273 Altgeld Hall, 1409 West Green Street, Urbana, IL 61801, USA
b Renaissance Technologies LLC, 600 Rt. 25A, East Setauket, NY 11733, USA |
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| Abstract: | Fix a sequence of positive integers (mn) and a sequence of positive real numbers (wn). Two closely related sequences of linear operators (Tn) are considered. One sequence has  given by the Lebesgue derivatives  . The other sequence has  given by the dyadic martingale  when (l−1)/n2?x<l/n2 for l=1,…,n2. We prove both positive and negative results concerning the convergence of  . |
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| Keywords: | Martingales Lebesque derivatives Large deviations |
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