scholarly journals Functional limit theorem for the self-intersection local time of the fractional Brownian motion

2019 ◽  
Vol 55 (1) ◽  
pp. 480-527 ◽  
Author(s):  
Arturo Jaramillo ◽  
David Nualart
Keyword(s):  
Brownian Motion ◽  
Limit Theorem ◽  
Fractional Brownian Motion ◽  
Local Time ◽  
Functional Limit Theorem ◽  
The Self ◽  
Functional Limit ◽  
Intersection 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.

On the local time of a recurrent random walk on ℤ²

2021 ◽  
Vol 105 (0) ◽  
pp. 69-78
Author(s):  
V. Bohun ◽  
A. Marynych
Keyword(s):  
Random Walk ◽  
Limit Theorem ◽  
Random Process ◽  
Local Time ◽  
Functional Limit Theorem ◽  
Functional Limit ◽  
Content Type ◽  
Finite Set ◽  
Number Of Visits ◽  
Recurrent Random Walk

We prove a functional limit theorem for the number of visits by a planar random walk on Z 2 \mathbb {Z}^2 with zero mean and finite second moment to the points of a fixed finite set P ⊂ Z 2 P\subset \mathbb {Z}^2 . The proof is based on the analysis of an accompanying random process with immigration at renewal epochs in case when the inter-arrival distribution has a slowly varying tail.

scholarly journals On the Self-Intersection Local Time of Subfractional Brownian Motion

2012 ◽  
Vol 2012 ◽  
pp. 1-27 ◽  
Author(s):  
Junfeng Liu ◽  
Zhihang Peng ◽  
Donglei Tang ◽  
Yuquan Cang
Keyword(s):  
Brownian Motion ◽  
White Noise ◽  
Local Time ◽  
Noise Analysis ◽  
The Self ◽  
White Noise Analysis ◽  
Intersection Local Time ◽  
Subfractional Brownian Motion

We study the problem of self-intersection local time ofd-dimensional subfractional Brownian motion based on the property of chaotic representation and the white noise analysis.

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