An Ideal Class to Construct Solutions for Skew Brownian Motion Equations

Fulgence Eyi Obiang (), Octave Moutsinga () and Youssef Ouknine ()
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Fulgence Eyi Obiang: Université des Sciences et Techniques de Masuku
Octave Moutsinga: Université des Sciences et Techniques de Masuku
Youssef Ouknine: Cadi Ayyad University

Journal of Theoretical Probability, 2022, vol. 35, issue 2, 894-916

Abstract: 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 ) .

Keywords: Class $$(\Sigma )$$ ( Σ ); Skew Brownian motion; Balayage formula; Honest time; Relative martingales; 60G07; 60G20; 60G46; 60G48 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10959-021-01078-5

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