An ideal class to construct solutions for skew Brownian motion equations

Fulgence Eyi Obiang, Octave Moutsinga, Youssef Ouknine

Published 2020-05-08Version 1

The present work focuses on the study of the $(\Sigma)$ class and consists of two main parts. In the first one, we extend the notion of semi-martingales of class $(\Sigma)$ to c\`adl\`ag semi-martingales whose the finite variational part is considered c\`adl\`ag instead of continuous. So, we propose a general framework dealing with such processes by extending some known results of the previous versions of the class $(\Sigma)$. The second part is dedicated to the study of continuous processes of the class $(\Sigma)$. More precisely, we first derive a series of new characterization results for such processes. Afterwards, we construct solutions for the skew Brownian motion equations using stochastic processes of the class $(\Sigma)$.