Boundary Feller-Dynkin processes associated with Laguerre processes and Pickrell diffusions

2025/09/21 by Alexander I. Bufetov, Bufetov, Alexander I., Yosuke Kawamoto +1
Economics, Econometrics and Finance · Mathematics · #60B20 #60J60 #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR) #Spectral Theory in Mathematical Physics #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2509.17045

openalex publication_date 2025/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we construct a Feller-Dynkin boundary process by applying the method of intertwiners to the coherent family, introduced in our previous work, of Laguerre processes with a fixed parameter. The corresponding boundary process is computed explicitly, and it turns out to be a deterministic dynamical system. Since the Pickrell diffusions that leave the Pickrell measure invariant are coherent with respect to the same projective system, we also obtain the stochastic boundary process associated with the coherent family of Pickrell diffusions.

Citations

• The intertwining property for β-Laguerre processes and integral operators for Jack polynomials
• The intertwining property for Laguerre processes with a fixed parameter
• On a gateway between the Laguerre process and dynamics on partitions
• Hua-Pickrell diffusions and Feller processes on the boundary of the graph of spectra
• Markov Processes on the Duals to Infinite-Dimensional Classical Lie\n Groups
• Intertwinings of beta-Dyson Brownian motions of different dimensions
• Strong solutions of non-colliding particle systems
• Markov dynamics on the Thoma cone: a model of time-dependent\n determinantal processes with infinitely many particles
• Wishart Processes
• Asymptotic Harmonic Analysis on the Space of Square Complex Matrices
• Dyson's Brownian motions, intertwining and interlacing

Related

• Hua-Pickrell diffusions and Feller processes on the boundary of the graph of spectra
• On the Feller-Dynkin and the Martingale Property of One-Dimensional Diffusions
• Long-time behavior for a class of Feller processes
• Multiple-particle diffusion processes from the viewpoint of Dunkl operators: relaxation to the steady state
• Differential Equations for Dyson Processes