TY - JOUR

T1 - Hitting Time Statistics and Extreme Value Theory

AU - Freitas, Ana Christina

AU - Freitas, Jorge

AU - Todd, Michael John

PY - 2010

Y1 - 2010

N2 - We consider discrete time dynamical systems and show the link between Hitting Time Statistics (the distribution of the first time points land in asymptotically small sets) and Extreme Value Theory (distribution properties of the partial maximum of stochastic processes). This relation allows to study Hitting Time Statisticswith tools from Extreme Value Theory, and vice versa. We apply these results to non-uniformly hyperbolic systems and prove that a multimodal map with an absolutely continuous invariant measure must satisfy the classical extreme value laws (with no extra condition on the speed of mixing, for example). We also give applications of our theory to higher dimensional examples, for which we also obtain classical extreme value laws and exponential hitting time statistics (for balls). We extend these ideas to the subsequent returns to asymptotically small sets, linking the Poisson statistics of both processes. © Springer-Verlag 2009.

AB - We consider discrete time dynamical systems and show the link between Hitting Time Statistics (the distribution of the first time points land in asymptotically small sets) and Extreme Value Theory (distribution properties of the partial maximum of stochastic processes). This relation allows to study Hitting Time Statisticswith tools from Extreme Value Theory, and vice versa. We apply these results to non-uniformly hyperbolic systems and prove that a multimodal map with an absolutely continuous invariant measure must satisfy the classical extreme value laws (with no extra condition on the speed of mixing, for example). We also give applications of our theory to higher dimensional examples, for which we also obtain classical extreme value laws and exponential hitting time statistics (for balls). We extend these ideas to the subsequent returns to asymptotically small sets, linking the Poisson statistics of both processes. © Springer-Verlag 2009.

U2 - 10.1007/s00440-009-0221-y

DO - 10.1007/s00440-009-0221-y

M3 - Article

SN - 0178-8051

VL - 147

SP - 675

EP - 710

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

IS - 3-4

ER -