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On the Euler--Maruyama scheme for degenerate stochastic differential equations with non-sticky condition
Dai Taguchi, Akihiro Tanaka · 2019-02-15 · via math.PR updates on arXiv.org

The aim of this paper is to study weak and strong convergence of the Euler--Maruyama scheme for a solution of one-dimensional degenerate stochastic differential equation $\mathrm{d} X_t=σ(X_t) \mathrm{d} W_t$ with non-sticky condition. For proving this, we first prove that the Euler--Maruyama scheme also satisfies non-sticky condition. As an example, we consider stochastic differential equation $\mathrm{d} X_t=|X_t|^α \mathrm{d} W_t$, $α\in (0,1/2)$ with non-sticky boundary condition and we give some remarks on CEV models in mathematical finance.

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