Abstract
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.
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AMS subject classification (2000)
60H10, 60H20, 60H30
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Halidias, N., Kloeden, P. A note on the Euler–Maruyama scheme for stochastic differential equations with a discontinuous monotone drift coefficient . Bit Numer Math 48, 51–59 (2008). https://doi.org/10.1007/s10543-008-0164-1
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DOI: https://doi.org/10.1007/s10543-008-0164-1