Kavli Affiliate: Jing Wang
| First 5 Authors: Peng Chen, Peng Chen, , ,
| Summary:
In this paper, we investigate the Milstein numerical scheme with step size
$eta$ for a stochastic differential equation driven by multiplicative Brownian
motion. Under some appropriate coefficient conditions, the continuous-time
system and its discrete Milstein scheme approximation each possess unique
invariant measures, which we denote by $pi$ and $pi_eta$ respectively. We
first establish a central limit theorem for the empirical measure $Pi_eta$,
a statistical consistent estimator of $pi_eta$. Subsequently, we derive
both normalized and self-normalized Cram’er-type moderate deviations.
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