On the time inhomogeneous skew Brownian motion
S. Bouhadou, Y. Ouknine
TL;DR
This paper constructs solutions for the inhomogeneous skew Brownian motion equation using the Balayage formula and investigates the behavior of solutions through a limit theorem.
Contribution
It introduces a novel construction method for inhomogeneous skew Brownian motion solutions utilizing the Balayage formula, extending previous studies.
Findings
Successful construction of solutions for inhomogeneous skew Brownian motion
Analysis of the limit behavior of solutions
Extension of prior theoretical results
Abstract
This paper is devoted to the construction of a solution for the "Inhomogenous skew Brownian motion" equation, which first appeared in a seminal paper by Sophie Weinryb, and recently, studied by \'{E}tor\'e and Martinez. Our method is based on the use of the Balayage formula. At the end of this paper we study a limit theorem of solutions.
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Taxonomy
TopicsStochastic processes and financial applications · Stochastic processes and statistical mechanics · Financial Risk and Volatility Modeling