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Constructing Self-Similar Martingales via Two Skorokhod Embeddings

Part of the Lecture Notes in Mathematics book series (SEMPROBAB,volume 2006)

Abstract

With the help of two Skorokhod embeddings, we construct martingales which enjoy the Brownian scaling property and the (inhomogeneous) Markov property. The second method necessitates randomization, but allows to reach any law with finite moment of order 1, centered, as the distribution of such a martingale at unit time. The first method does not necessitate randomization, but an additional restriction on the distribution at unit time is needed.

  • Convex order
  • Hardy-Littlewood functions
  • Karamata’s representation theorem
  • Schauder fixed point theorem
  • Self-similar martingales
  • Skorokhod embeddings

2000 MSC: Primary: 60EXX, 60G18, 60G40, 60G44, 60J25, 60J65; Secondary: 26A12, 47H10

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Hirsch, F., Profeta, C., Roynette, B., Yor, M. (2011). Constructing Self-Similar Martingales via Two Skorokhod Embeddings. In: Donati-Martin, C., Lejay, A., Rouault, A. (eds) Séminaire de Probabilités XLIII. Lecture Notes in Mathematics(), vol 2006. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15217-7_21

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