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Reciprocal Processes: A Stochastic Analysis Approach

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Modern Stochastics and Applications

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 90))

Abstract

Reciprocal processes, whose concept can be traced back to E. Schrödinger, form a class of stochastic processes constructed as mixture of bridges. They are Markov fields indexed by a time interval. We discuss here a new unifying approach to characterize several types of reciprocal processes via duality formulae on path spaces: The case of reciprocal processes with continuous paths associated to Brownian diffusions and the case of pure jump reciprocal processes associated to counting processes are treated. This chapter is based on joint works with M. Thieullen, R. Murr, and C. Léonard.

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Acknowledgements

The author gratefully acknowledges the Organizing Committee of the International Conference Modern Stochastics: Theory and Applications III for the very pleasant and interesting meeting. The author is also grateful to an anonymous Referee for the constructive critics.

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Authors and Affiliations

  1. Institut für Mathematik der Universität Potsdam, Am Neuen Palais 10, 14469, Potsdam, Germany

    Sylvie Rœlly

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  1. Sylvie Rœlly
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Correspondence to Sylvie Rœlly .

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Editors and Affiliations

  1. Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    Volodymyr Korolyuk

  2. Laboratoire de Mathématiques Appliquées, Université de Technologie de Compiègne, Compiegne Cedex, France

    Nikolaos Limnios

  3. Dept. of Probability, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

    Yuliya Mishura

  4. Dept.of Probability, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

    Lyudmyla Sakhno

  5. Dept.of Probability, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

    Georgiy Shevchenko

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Rœlly, S. (2014). Reciprocal Processes: A Stochastic Analysis Approach. In: Korolyuk, V., Limnios, N., Mishura, Y., Sakhno, L., Shevchenko, G. (eds) Modern Stochastics and Applications. Springer Optimization and Its Applications, vol 90. Springer, Cham. https://doi.org/10.1007/978-3-319-03512-3_4

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