Abstract
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.
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Acknowledgments
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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Guo, H., Philipowski, R. & Thalmaier, A. Martingales on Manifolds with Time-Dependent Connection. J Theor Probab 28, 1038–1062 (2015). https://doi.org/10.1007/s10959-013-0536-6
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DOI: https://doi.org/10.1007/s10959-013-0536-6