Abstract
We introduce a semi-implicit Milstein approximation scheme for some classes of non-colliding particle systems modeled by systems of stochastic differential equations with non-constant diffusion coefficients. We show that the scheme converges at the rate of order 1 in the mean-square sense.
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This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 101.03-2017.316. The paper was completed during a scientific stay of the second author at the Vietnam Institute for Advanced Study in Mathematics (VIASM), whose hospitality is gratefully appreciated.
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Luong, DT., Ngo, HL. Semi-implicit Milstein approximation scheme for non-colliding particle systems. Calcolo 56, 25 (2019). https://doi.org/10.1007/s10092-019-0319-2
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DOI: https://doi.org/10.1007/s10092-019-0319-2
Keywords
- Dyson Brownian motion
- Milstein scheme
- Particle system
- Stochastic differential equation
- Strong approximation