2021/04/13 by Dom Brockington, Brockington, Dom, Jon Warren +1 · 1 citation
Economics, Econometrics and Finance · Mathematics · #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.2104.06482
openalex publication_date 2021/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a diffusion in ℝn whose coordinates each behave as one-dimensional Brownian motions, that behave independently when apart, but have a sticky interaction when they meet. The diffusion in ℝn can be viewed as the n-point motion of a stochastic flow of kernels. We derive the Kolmogorov backwards equation and show that for a specific choice of interaction it can be solved exactly with the Bethe ansatz. We then use our formulae to study the behaviour of the flow of kernels for the exactly solvable choice of interaction.