Sharp Error Terms for Return Time Statistics under Mixing Conditions

ar X iv : 0 81 2 . 10 16 v 1 [ m at h . PR ] 4 D ec 2 00 8 Sharp error terms for return time statistics under mixing conditions

We describe the statistics of repetition times of a string of symbols in a stochastic process. Denote by τA the time elapsed until the process spells the finite string A and by SA the number of consecutive repetitions of A. We prove that, if the length of the string grows unbondedly, (1) the distribution of τA, when the process starts with A, is well approximated by a certain mixture of the poi...

Statistics and Error Terms of Occurrence Times in Mixing Processes

Return Time Statistics via Inducing

We prove that return time statistics of a dynamical system do not change if one passes to an induced (i.e. rst return) map. We apply this to show exponential return time statistics in i) smooth interval maps with nowhere{dense critical orbits and ii) certain interval maps with neutral xed points. The method also applies to iii) certain quadratic maps of the complex plane.

Sharp forms of Nevanlinna error terms in differential equations

Sharp versions of some classical results in differential equations are given. Main results consists of a Clunie and a Mohon’ko type theorems, both with sharp forms of error terms. The sharpness of these results is discussed and some applications to nonlinear differential equations are given in the conluding remarks. Moreover, a short introduction on the connection between Nevanlinna theory and ...

Regularity under Sharp Anisotropic General Growth Conditions

We prove boundedness of minimizers of energy-functionals, for instance of the anisotropic type (1.1) below, under sharp assumptions on the exponents pi in terms of p ∗: the Sobolev conjugate exponent of p; i.e., p∗ = np n−p , 1 p = 1 n Pn i=1 1 pi . As a consequence, by mean of regularity results due to Lieberman [21], we obtain the local Lipschitz-continuity of minimizers under sharp assumptio...