A Sharp and Strict Lp-Inequality for Stochastic Integrals

  • Burgess DavisEmail author
  • Renming Song
Part of the Selected Works in Probability and Statistics book series (SWPS)


Let (Ω, F, P) be a complete probability space and (F t )t ≥ 0 a nondecreasing right-continuous family of sub-σ-fields of F where F 0 contains all AF with P(A) = 0. Suppose that M = (M t )t ≥ 0 is a real martingale adapted to (F t )t ≥ 0 such that almost all of the paths of M are right-continuous on [0, ∞) and have left limits on (0, ∞). Let V = (V t )t ≥ 0 be a predictable process with values in [−1, 1] and denote by N= VM the stochastic integral of V with respect to M: N is an adapted right-continuous process with left limits on (0, ∞) such that
$${N_t} = \int_{\left[ {0,\,t} \right]} {{V_s}\,d{M_s}} \,a.s.$$


Strict Inequality Stochastic Integral Select Work Predictable Process Left Limit 
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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Mathematics and Department of StatisticsPurdue UniversityWest LafayetteUSA
  2. 2.Department of MathematicsUniversity of IllinoisUrbanaUSA

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