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An Ideal Class to Construct Solutions for Skew Brownian Motion Equations

Author

Listed:
  • Fulgence Eyi Obiang

    (Université des Sciences et Techniques de Masuku)

  • Octave Moutsinga

    (Université des Sciences et Techniques de Masuku)

  • Youssef Ouknine

    (Cadi Ayyad University
    Hassan II Academy of Sciences and Technologies
    Africa Business School, Mohammed VI Polytechnic)

Abstract

This paper contributes to the study of stochastic processes of the class $$(\Sigma )$$ ( Σ ) . 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 $$(\Sigma )$$ ( Σ ) . 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 $$(\Sigma )$$ ( Σ ) .

Suggested Citation

  • Fulgence Eyi Obiang & Octave Moutsinga & Youssef Ouknine, 2022. "An Ideal Class to Construct Solutions for Skew Brownian Motion Equations," Journal of Theoretical Probability, Springer, vol. 35(2), pages 894-916, June.
    • Handle: RePEc:spr:jotpro:v:35:y:2022:i:2:d:10.1007_s10959-021-01078-5
    DOI: 10.1007/s10959-021-01078-5
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    References listed on IDEAS

    as
    1. Nikeghbali, Ashkan, 2006. "A class of remarkable submartingales," Stochastic Processes and their Applications, Elsevier, vol. 116(6), pages 917-938, June.
    2. Ashkan Nikeghbali, 2006. "Multiplicative Decompositions and Frequency of Vanishing of Nonnegative Submartingales," Journal of Theoretical Probability, Springer, vol. 19(4), pages 931-949, December.
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