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