| Abstract: |
| In this talk, we consider a discrete approximation for non-colliding particle systems such as Dyson`s Brownian motions with drift and Brownian particle systems with nearest neighbour repulsion. As a numerical analysis of a solution to stochastic differential equation, one often approximates it by using the ``explicit`` Euler-Maruyama scheme. However, unfortunately, the explicit scheme does not preserve the non-colliding property of non-colliding particle systems. Therefore, we introduce implicit Euler-Maruyama scheme which preserve the non-colliding property, and study its rate of convergence in $L^p$-norm. |
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