2023/02/06 by Wajdi Touhami, Touhami, Wajdi
Economics, Econometrics and Finance · Mathematics · #60H10 #60J60 #60J65 #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2302.03125
openalex publication_date 2023/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Starting with a Brownian motion, we define and study a novel diffusion process by combining stickiness and oscillation properties. The associated stochastic differential equation, resolvent and semigroup are provided. Also the trivariate density of position, local time and occupation time of this diffusion is obtained explicitly. Furthermore, we give a construction of two Brownian motions with drift and scaling whose difference is an oscillating sticky Brownian motion, up to a multiplicative constant.