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An Ideal Class to Construct Solutions for Skew Brownian Motion Equations

Journal of Theoretical Probability volume 35, pages 894–916 (2022)Cite this article

Abstract

This paper contributes to the study of stochastic processes of the class \((\Sigma )\). First, we extend the notion of the above-mentioned class to càdlàg semi-martingales, whose finite variation part is considered càdlàg instead of continuous. Thus, we present some properties and propose a method to characterize such stochastic processes. Second, we investigate continuous processes of the class \((\Sigma )\). More precisely, we derive a series of new characterization results. In addition, we construct solutions for skew Brownian motion equations using continuous stochastic processes of the class \((\Sigma )\).

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Acknowledgements

We thank the referee for the careful reading of the paper and for valuable remarks.

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Authors and Affiliations

  1. URMI Laboratory, Département de Mathématiques et Informatique, Faculté des Sciences, Université des Sciences et Techniques de Masuku, BP 943, Franceville, Gabon

    Fulgence Eyi Obiang & Octave Moutsinga

  2. LIBMA Laboratory, Department of Mathematics, Faculty of Sciences Semlalia, Cadi Ayyad University, P.B.O. 2390, Marrakech, Morocco

    Youssef Ouknine

  3. Hassan II Academy of Sciences and Technologies, Rabat, Morocco

    Youssef Ouknine

  4. Africa Business School, Mohammed VI Polytechnic, Lot 660, HayMoulay Rachid, P.B.O. 43150, Benguerir, Morocco

    Youssef Ouknine

Authors
  1. Fulgence Eyi Obiang
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  2. Octave Moutsinga
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  3. Youssef Ouknine
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Correspondence to Fulgence Eyi Obiang.

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Eyi Obiang, F., Moutsinga, O. & Ouknine, Y. An Ideal Class to Construct Solutions for Skew Brownian Motion Equations. J Theor Probab 35, 894–916 (2022). https://doi.org/10.1007/s10959-021-01078-5

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  • DOI: https://doi.org/10.1007/s10959-021-01078-5

Keywords

  • Class \((\Sigma )\)
  • Skew Brownian motion
  • Balayage formula
  • Honest time
  • Relative martingales

Mathematics Subject Classification

  • 60G07
  • 60G20
  • 60G46
  • 60G48