Scaling limit of the local time of the reflected (1,2)-random walk

2019 ◽  
Vol 155 ◽  
pp. 108578
Author(s):  
Hui Yang
Keyword(s):  
Random Walk ◽  
Local Time ◽  
Scaling Limit

scholarly journals Scaling limit of local time of Sinai’s random walk

2015 ◽  
Vol 10 (6) ◽  
pp. 1313-1324
Author(s):  
Wenming Hong ◽  
Hui Yang ◽  
Ke Zhou
Keyword(s):  
Random Walk ◽  
Local Time ◽  
Scaling Limit

Self-avoiding random walk: A Brownian motion model with local time drift

1987 ◽  
Vol 74 (2) ◽  
pp. 271-287 ◽  
Author(s):  
J. R. Norris ◽  
L. C. G. Rogers ◽  
David Williams
Keyword(s):  
Brownian Motion ◽  
Random Walk ◽  
Local Time ◽  
Motion Model ◽  
Time Drift ◽  
Brownian Motion Model

scholarly journals On the scaling limit of loop-erased random walk excursion

2012 ◽  
Vol 50 (2) ◽  
pp. 331-357
Author(s):  
Fredrik Johansson Viklund
Keyword(s):  
Random Walk ◽  
Scaling Limit

Limit distributions for the Bernoulli meander

1995 ◽  
Vol 32 (2) ◽  
pp. 375-395 ◽  
Author(s):  
Lajos Takács
Keyword(s):  
Random Walk ◽  
Local Time ◽  
Limit Behavior ◽  
Explicit Formulas ◽  
Limit Distributions ◽  
Brownian Meander

This paper is concerned with the distibutions and the moments of the area and the local time of a random walk, called the Bernoulli meander. The limit behavior of the distributions and the moments is determined in the case where the number of steps in the random walk tends to infinity. The results of this paper yield explicit formulas for the distributions and the moments of the area and the local time for the Brownian meander.

scholarly journals On the local time of random walk on the 2-dimensional comb

2011 ◽  
Vol 121 (6) ◽  
pp. 1290-1314 ◽  
Author(s):  
Endre Csáki ◽  
Miklós Csörgő ◽  
Antónia Földes ◽  
Pál Révész
Keyword(s):  
Random Walk ◽  
Local Time

Convergence to the local time of Brownian meander

2019 ◽  
Vol 29 (3) ◽  
pp. 149-158 ◽  
Author(s):  
Valeriy. I. Afanasyev
Keyword(s):  
Random Walk ◽  
Limit Theorem ◽  
Local Time ◽  
Random Processes ◽  
Functional Limit Theorem ◽  
Zero Drift ◽  
Functional Limit ◽  
Brownian Meander

Abstract Let {Sn, n ≥ 0} be integer-valued random walk with zero drift and variance σ2. Let ξ(k, n) be number of t ∈ {1, …, n} such that S(t) = k. For the sequence of random processes $\begin{array}{} \xi(\lfloor u\sigma \sqrt{n}\rfloor,n) \end{array}$ considered under conditions S1 > 0, …, Sn > 0 a functional limit theorem on the convergence to the local time of Brownian meander is proved.

scholarly journals Long random walk excursions and local time

1992 ◽  
Vol 41 (2) ◽  
pp. 181-190
Author(s):  
Miklós Csörgő ◽  
Pál Révész
Keyword(s):  
Random Walk ◽  
Local Time

scholarly journals Intrinsic random walks in Riemannian and sub-Riemannian geometry via volume sampling

2018 ◽  
Vol 24 (3) ◽  
pp. 1075-1105
Author(s):  
Andrei Agrachev ◽  
Ugo Boscain ◽  
Robert Neel ◽  
Luca Rizzi
Keyword(s):  
Random Walk ◽  
Riemannian Manifolds ◽  
Riemannian Geometry ◽  
Stochastic Analysis ◽  
Scaling Limit ◽  
Primary Motivation ◽  
Infinitesimal Generators ◽  
Integral Curves ◽  
Parabolic Scaling ◽  
Riemannian Case

We relate some constructions of stochastic analysis to differential geometry, via random walk approximations. We consider walks on both Riemannian and sub-Riemannian manifolds in which the steps consist of travel along either geodesics or integral curves associated to orthonormal frames, and we give particular attention to walks where the choice of step is influenced by a volume on the manifold. A primary motivation is to explore how one can pass, in the parabolic scaling limit, from geodesics, orthonormal frames, and/or volumes to diffusions, and hence their infinitesimal generators, on sub-Riemannian manifolds, which is interesting in light of the fact that there is no completely canonical notion of sub-Laplacian on a general sub-Riemannian manifold. However, even in the Riemannian case, this random walk approach illuminates the geometric significance of Ito and Stratonovich stochastic differential equations as well as the role played by the volume.

scholarly journals Maximal Local Time of a d-dimensional Simple Random Walk on Subsets

2005 ◽  
Vol 18 (3) ◽  
pp. 687-717 ◽  
Author(s):  
Endre Csáki ◽  
Antönia Földes ◽  
Pál Révész
Keyword(s):  
Random Walk ◽  
Local Time ◽  
Simple Random Walk
Sign in / Sign up

Export Citation Format

Share Document