On Maximal Inequalities for Purely Discontinuous Martingales in Infinite Dimensions

  • Carlo Marinelli
  • Michael Röckner
Part of the Lecture Notes in Mathematics book series (LNM, volume 2123)


The purpose of this paper is to give a survey of a class of maximal inequalities for purely discontinuous martingales, as well as for stochastic integral and convolutions with respect to Poisson measures, in infinite dimensional spaces. Such maximal inequalities are important in the study of stochastic partial differential equations with noise of jump type.


Stochastic Integral Stochastic Partial Differential Equation Maximal Inequality Poisson Random Measure Stochastic Convolution 
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A large part of the work for this paper was carried out during visits of the first-named author to the Interdisziplinäres Zentrum für Komplexe Systeme, Universität Bonn, invited by S. Albeverio. The second-named author is supported by the DFG through the SFB 701.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of MathematicsUniversity College LondonLondonUK
  2. 2.Fakultät für MathematikUniversität BielefeldBielefeldGermany

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