A note on the Euler–Maruyama scheme for stochastic differential equations with a discontinuous monotone drift coefficient
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It is shown that the Euler–Maruyama scheme applied to a stochastic differential equation with a discontinuous monotone drift coefficient, such as a Heaviside function, and additive noise converges strongly to a solution of the stochastic differential equation with the same initial condition. The proof uses upper and lower solutions of the stochastic differential equations and the Euler–Maruyama scheme.
Key wordsdiscontinuous monotone drift Euler–Maruyama scheme upper and lower solutions
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