Abstract:Strong invariance principles describe the error term of a Brownian approximation of the partial sums of a stochastic process. While these strong approximation results have many applications, the results for continuous-time settings have been limited. In this paper, we obtain strong invariance principles for a broad class of ergodic Markov processes. The main results rely on ergodicity requirements and an application of Nummelin splitting for continuous-time processes. Strong invariance principles provide a uni… Show more
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