Ergodicity of Stochastic Shell Models Driven by Pure Jump Noise

@article{Bessaih2016ErgodicityOS,
  title={Ergodicity of Stochastic Shell Models Driven by Pure Jump Noise},
  author={Hakima Bessaih and Erika Hausenblas and Paul Andr{\'e} Razafimandimby},
  journal={SIAM J. Math. Analysis},
  year={2016},
  volume={48},
  pages={1423-1458}
}
In the present paper we study a stochastic evolution equation for shell (SABRA \& GOY) models with pure jump \levy noise $L=\sum_{k=1}^\infty l_k(t)e_k$ on a Hilbert space $\h$. Here $\{l_k, k\in \mathbb{N}\}$ is a family of independent and identically distributed (i.i.d.) real-valued pure jump \levy processes and $\{e_k, k\in \mathbb{N}\}$ is an orthonormal basis of $\h$. We mainly prove that the stochastic system has a unique invariant measure. For this aim we show that if the \levy measure… CONTINUE READING
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