Abstract
We propose a stochastic energy balance differential equation with multiplicative Gaussian noise, which better captures the influence of the atmosphere as external noise on climate change. Meanwhile, we apply the Milstein method with stronger convergence to approximate the stochastic climate change trajectory. Further, the numerical approach can efficiently calculate two exit concepts: the mean first exit time and the first escape probability. These two quantities are used to examine the transition of the climate from one state to another. For global warming of [Formula: see text]C and [Formula: see text]C, we find that the enhanced noise intensity is more likely to induce a shorter mean first exit time or a higher first escape probability. These results provide important insights into the underlying mechanisms of climate change for global warming.
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