| Título: | Laws of the Iterated Logarithm for Triple Intersections of Three Dimensional Random Walks |
| Autores: | Rosen, Jay; College of Staten Island, CUNY |
| Fecha: | 1997-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
Mathematics random walks, intersections 60J15, 60F99 |
| Descripción: | Let $X = X_n, X' = X'_n$, and $X'' = X''_n$, $n\geq 1$, be three independent copies of a symmetric three dimensional random walk with $E(|X_1|^{2}\log_+ |X_1|)$ finite. In this paper we study the asymptotics of $I_n$, the number of triple intersections up to step $n$ of the paths of $X, X'$ and $X''$ as $n$ goes to infinity. Our main result says that the limsup of $I_n$ divided by $\log (n) \log_3 (n)$ is equal to $1 \over \pi |Q|$, a.s., where $Q$ denotes the covariance matrix of $X_1$. A similar result holds for $J_n$, the number of points in the triple intersection of the ranges of $X, X'$ and $X''$ up to step $n$. |
| Idioma: | Inglés |
1 Lévy Classes and Self-Normalization por Khoshnevisan, Davar; University of Utah | 6 Time-Space Analysis of the Cluster-Formation in Interacting Diffusions por Fleischmann, Klaus; Weierstrass Institute for Applied Analysis and Stochastics,Greven, Andreas; Universitat Erlangen-Nurnberg |
2 Hausdorff Dimension of Cut Points for Brownian Motion por Lawler, Gregory F.; Duke University and Cornell University | 7 Conditional Moment Representations for Dependent Random Variables por Bryc, Wlodzimierz; University of Cincinnati |
3 Eigenvalue Expansions for Brownian Motion with an Application to Occupation Times por Bass, Richard F.; University of Washington,Burdzy, Krzysztof; University of Washington | 8 Almost Sure Exponential Stability of Neutral Differential Difference Equations with Damped Stochastic Perturbations por Liao, Xiao Xin; University of Strathclyde,Mao, Xuerong; University of Strathclyde |
4 Random Discrete Distributions Derived from Self-Similar Random Sets por Pitman, Jim; University of California, Berkeley,Yor, Marc; Université Pierre et Marie Curie | 9 Quantitative Bounds for Convergence Rates of Continuous Time Markov Processes por Roberts, Gareth O.; University of Cambridge,Rosenthal, Jeffrey S.; University of Toronto |
5 A Microscopic Model for the Burgers Equation and Longest Increasing Subsequences por Seppäläinen, Timo; Iowa State University | 10 Metastability of the Three Dimensional Ising Model on a Torus at Very Low Temperatures por Ben Arous, Gérard; Ecole Normale Supérieure,Cerf, Raphaël; Université Paris Sud |