• Corpus ID: 119321658

Stochastic averaging for multiscale Markov processes with an application to a Wright-Fisher model with fluctuating selection

  title={Stochastic averaging for multiscale Markov processes with an application to a Wright-Fisher model with fluctuating selection},
  author={Martin Hutzenthaler and Peter Pfaffelhuber and C. H. Printz},
  journal={arXiv: Probability},
Let $Z = (Z_t)_{t\in[0,\infty)}$ be an ergodic Markov process and, for every $n\in\mathbb{N}$, let $Z^n = (Z_{n^2 t})_{t\in[0,\infty)}$ drive a process $X^n$. Classical results show under suitable conditions that the sequence of non-Markovian processes $(X^n)_{n\in\mathbb{N}}$ converges to a Markov process and give its infinitesimal characteristics. Here, we consider a general sequence $(Z^n)_{n\in\mathbb{N}}$. Using a general result on stochastic averaging from [Kur92], we derive conditions… 
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