Minh-Thang Do | Searcharxiv

arXiv2024

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

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 $\mathbb{R}^{d}$ instead of the Weyl chamber $\mathbb{W}$, offering improved computational efficiency.

math.PR↗

arXiv2023

Tamed-adaptive Euler-Maruyama approximation for SDEs with superlinearly growing and piecewise continuous drift, superlinearly growing and locally Hölder continuous diffusion

In this paper, we consider stochastic differential equations whose drift coefficient is superlinearly growing and piece-wise continuous, and whose diffusion coefficient is superlinearly growing and locally Hölder continuous. We first prove the existence and uniqueness of the solution to such stochastic differential equations and then propose a tamed-adaptive Euler-Maruyama approximation scheme. We study the rate of convergence in the $L^1$-norm of the scheme in both finite and infinite time intervals.

math.PR↗