Pesin's formula relates the entropy of a dynamical system with its positiveLyapunov exponents. It is well known, that this formula holds true for randomdynamical systems on a compact Riemannian manifold with invariant probabilitymeasure which is absolutely continuous with respect to the Lebesgue measure. Wewill show that this formula remains true for random dynamical systems on $R^d$which have an invariant probability measure absolutely continuous to theLebesgue measure on $R^d$. Finally we will show that a broad class ofstochastic flows on $R^d$ of a Kunita type satisfies Pesin's formula.
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机译：Pesin公式将动力学系统的熵与其正Lyapunov指数联系起来。众所周知，该公式对于具有不变概率测度的紧致黎曼流形上的随机动力系统成立，该概率测度相对于Lebesgue测度是绝对连续的。我们将证明该公式对于$ R ^ d $上的随机动力学系统仍然成立，该系统具有与$ R ^ d $上的Lebesgue测度绝对连续的不变概率测度。最终，我们将证明Kunita类型的$ R ^ d $上的广泛随机流满足Pesin公式。
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