Filtered data based estimators for stochastic processes driven by colored noise
CoRR(2023)
摘要
We consider the problem of estimating unknown parameters in stochastic
differential equations driven by colored noise, which we model as a sequence of
Gaussian stationary processes with decreasing correlation time. We aim to infer
parameters in the limit equation, driven by white noise, given observations of
the colored noise dynamics. We consider both the maximum likelihood and the
stochastic gradient descent in continuous time estimators, and we propose to
modify them by including filtered data. We provide a convergence analysis for
our estimators showing their asymptotic unbiasedness in a general setting and
asymptotic normality under a simplified scenario.
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