## Escape Rates for a Conditioned 2-dimensional Brownian Motion and Recurrence Results for Analytic Zygmund Functions with Applications |

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### Contents

Escape Rates for a Conditioned 2Dimensional Brownian | 8 |

An Application to A | 21 |

Recurrence Properties for Nondifferentiable Functions in | 33 |

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### Common terms and phrases

2-dimensional Brownian motion a-finite i-measure a-finite linear Hausdorff a.e. non-differentiable absolutely continuous Ahf(e,e Anderson and Pitt angle with vertex Bloch function Bloch space Borel-Cantelli theorem Brownian motion conditioned Chapter clogr complex conditioned process Consequently constant in Lemma continuous functions denote dense difference quotient dimensional random walk escape rate estimates finite accumulation point functions with period G P2 given S0(u hits implies increasing function inside the unit integral test interval irregular 1-set jump lacunary series Lebesgue measure left side linear Hausdorff measure logr logT measure functions mi(Z multiplication operators partial sums probability measure Proof Proposition 4.3 provides lower bounds purely singular continuous Q'(AjAk radial rate to infinity real function real-valued functions recurrence results relating the difference Rogers and Taylor scale function singular continuous spectrum Sn(u Souslin set spectral measure Spectral Theory Stoltz angle suffices Theorem 5.3 Theory of Multiplication unit disk upper bound