An ideal class to construct solutions for skew Brownian motion equations

2020/05/08 by Obiang, Fulgence Eyi, Moutsinga, Octave, Ouknine, Youssef
#60G07 #60G20 #60G46 #60G48 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2005.04030

Abstract

This paper contributes to the study of stochastic processes of the class (Σ). First, we extend the notion of the above-mentioned class to càdlàg semi-martingales, whose finite variational 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 (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 (Σ).

Related

• Characterization of a new class of stochastic processes including all known extensions of the class (Σ)
• A new class of stochastic processes with great potential for interesting applications
• Stochastic differential equations driven by relative martingales
• Resolution of the skew Brownian motion equations with stochastic calculus for signed measures
• New contributions to the study of stochastic processes of the class (Σ)