Strong solution and approximation of time-dependent radial Dunkl processes with multiplicative noise

2024/10/14 by Minh-Thang Do, Do, Minh-Thang, Hoang-Long Ngo +3
Computer Science · Mathematics · #17B22 #60H35 #65C30 #91G60 #FOS: Mathematics #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #Numerical Analysis (math.NA) #Probability (math.PR) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2410.10457

openalex publication_date 2024/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the strong existence and uniqueness of solutions within a Weyl chamber for a class of time-dependent particle systems driven by multiplicative noise. This class includes well-known processes in physics and mathematical finance. We propose a method to prove the existence of negative moments for the solutions. This result allows us to analyze two numerical schemes for approximating the solutions. The first scheme is a θ-Euler--Maruyama scheme, which ensures that the approximated solution remains within the Weyl chamber. The second scheme is a truncated θ-Euler--Maruyama scheme, which produces values in ℝ^d instead of the Weyl chamber \mathbbW, offering improved computational efficiency.

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