Transient random walk in ${\mathbb Z}^2$ with stationary orientations

Françoise Pène

Displaying similar documents to “Transient random walk in $ℤ^{2}$ with stationary orientations”

Central limit theorem for sampled sums of dependent random variables

Nadine Guillotin-Plantard, Clémentine Prieur (2010)

ESAIM: Probability and Statistics

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We prove a central limit theorem for linear triangular arrays under weak dependence conditions. Our result is then applied to dependent random variables sampled by a $ℤ$ -valued transient random walk. This extends the results obtained by [N. Guillotin-Plantard and D. Schneider, (2003) 477–497]. An application to parametric estimation by random sampling is also provided.

Limit theorems for U-statistics indexed by a one dimensional random walk

Nadine Guillotin-Plantard, Véronique Ladret (2005)

ESAIM: Probability and Statistics

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Let ${(S_{n})}_{n \geq 0}$ be a $ℤ$ -random walk and ${(ξ_{x})}_{x \in ℤ}$ be a sequence of independent and identically distributed $ℝ$ -valued random variables, independent of the random walk. Let $h$ be a measurable, symmetric function defined on $ℝ^{2}$ with values in $ℝ$ . We study the weak convergence of the sequence $𝒰_{n}, n \in ℕ$ , with values in $D [0, 1]$ the set of right continuous real-valued functions with left limits, defined by $\sum_{i, j = 0}^{[n t]} h (ξ_{S_{i}}, ξ_{S_{j}}), t \in [0, 1] .$ Statistical applications are presented, in particular we prove a strong law of large numbers for...

On the Brunk-Chung type strong law of large numbers for sequences of blockwise -dependent random variables

Le Van Thanh (2006)

ESAIM: Probability and Statistics

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For a sequence of blockwise -dependent random variables {≥ 1}, conditions are provided under which ${lim}_{n \to \infty} (\sum_{i = 1}^{n} X_{i}) / b_{n} = 0$ almost surely where {≥ 1} is a sequence of positive constants. The results are new even when . As special case, the Brunk-Chung strong law of large numbers is obtained for sequences of independent random variables. The current work also extends results of Móricz [ (1987) 709–715], and Gaposhkin [. (1994) 804–812]. The sharpness of the results is illustrated by examples. ...

Central limit theorem for the excited random walk in dimension $d \geq 2$ .

Bérard, Jean, Ramirez, Alejandro (2007)

Electronic Communications in Probability [electronic only]

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Perturbing transient random walk in a random environment with cookies of maximal strength

Elisabeth Bauernschubert (2013)

Annales de l'I.H.P. Probabilités et statistiques

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We consider a left-transient random walk in a random environment on $ℤ$ that will be disturbed by cookies inducing a drift to the right of strength 1. The number of cookies per site is i.i.d. and independent of the environment. Criteria for recurrence and transience of the random walk are obtained. For this purpose we use subcritical branching processes in random environments with immigration and formulate criteria for recurrence and transience for these processes.

Random walk in random environment with asymptotically zero perturbation

M.V. Menshikov, Andrew R. Wade (2006)

Journal of the European Mathematical Society

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We give criteria for ergodicity, transience and null-recurrence for the random walk in random environment on $ℤ^{+} = {0, 1, 2, \dots}$ , with reflection at the origin, where the random environment is subject to a vanishing perturbation. Our results complement existing criteria for random walks in random environments and for Markov chains with asymptotically zero drift, and are significantly different from the previously studied cases. Our method is based on a martingale technique—the method of Lyapunov functions. ...

A log-scale limit theorem for one-dimensional random walks in random environments.

Roitershtein, Alexander (2005)

Electronic Communications in Probability [electronic only]

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An invariance principle in $L^{2} [0, 1]$ for non stationary $ϕ$ -mixing sequences

Paulo Eduardo Oliveira, Charles Suquet (1995)

Commentationes Mathematicae Universitatis Carolinae

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Invariance principle in $L^{2} (0, 1)$ is studied using signed random measures. This approach to the problem uses an explicit isometry between $L^{2} (0, 1)$ and a reproducing kernel Hilbert space giving a very convenient setting for the study of compactness and convergence of the sequence of Donsker functions. As an application, we prove a $L^{2} (0, 1)$ version of the invariance principle in the case of $ϕ$ -mixing random variables. Our result is not available in the $D (0, 1)$ -setting.

Displaying similar documents to “Transient random walk in ℤ 2 with stationary orientations”

Displaying similar documents to “Transient random walk in $ℤ^{2}$ with stationary orientations”