Journal of Theoretical Probability

, Volume 28, Issue 3, pp 1038–1062 | Cite as

Martingales on Manifolds with Time-Dependent Connection

  • Hongxin Guo
  • Robert Philipowski
  • Anton Thalmaier


We define martingales on manifolds with time-dependent connection, extending in this way the theory of stochastic processes on manifolds with time-changing geometry initiated by Arnaudon et al. (C R Acad Sci Paris Ser I 346:773–778, 2008). We show that some, but not all, properties of martingales on manifolds with a fixed connection extend to this more general setting.


Stochastic analysis on manifolds Time-dependent geometry Martingales 

Mathematics Subject Classification (2010)

53C44 58J65 60G44 60G48 



The first author was supported by NSFC (Grants No. 11001203 and 11171143) and Zhejiang Provincial Natural Science Foundation of China (Project No. LY13A010009).


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Hongxin Guo
    • 1
  • Robert Philipowski
    • 2
  • Anton Thalmaier
    • 2
  1. 1.School of Mathematics and Information ScienceWenzhou UniversityWenzhouChina
  2. 2.Mathematics Research Unit, FSTCUniversity of LuxembourgLuxembourgGrand Duchy of Luxembourg

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