Random Walks on the Half-Axis. II. Limit Distributions of Boundary Functionals

1982 ◽  
Vol 26 (3) ◽  
pp. 452-467
Author(s):  
V. M. Shurenkov
Keyword(s):  
Random Walks ◽  
Axis Ii ◽  
Limit Distributions ◽  
Half Axis ◽  
Boundary Functionals

scholarly journals Area of Brownian Motion with Generatingfunctionology

2003 ◽  
Vol DMTCS Proceedings vol. AC,... (Proceedings) ◽  
Author(s):  
Michel Nguyên Thê
Keyword(s):  
Brownian Motion ◽  
Random Walks ◽  
Generating Functions ◽  
Limit Distributions ◽  
Dyck Paths ◽  
Different Types ◽  
International Audience

International audience This paper gives a survey of the limit distributions of the areas of different types of random walks, namely Dyck paths, bilateral Dyck paths, meanders, and Bernoulli random walks, using the technology of generating functions only.

Certain boundary functionals for Markov random walks

1978 ◽  
Vol 23 (2) ◽  
pp. 169-175
Author(s):  
V. A. Ivanov ◽  
G. I. Ivchenko
Keyword(s):  
Random Walks ◽  
Markov Random ◽  
Boundary Functionals

scholarly journals Limit distributions of random walks on stochastic matrices

2014 ◽  
Vol 124 (4) ◽  
pp. 603-612
Author(s):  
SANTANU CHAKRABORTY ◽  
ARUNAVA MUKHERJEA
Keyword(s):  
Random Walks ◽  
Stochastic Matrices ◽  
Limit Distributions

scholarly journals Limit Distributions of Directionally Reinforced Random Walks

1998 ◽  
Vol 134 (2) ◽  
pp. 367-383 ◽  
Author(s):  
Lajos Horváth ◽  
Qi-Man Shao
Keyword(s):  
Random Walks ◽  
Limit Distributions ◽  
Reinforced Random Walks

scholarly journals Limit Theorems for a Generalized Feller Game

2013 ◽  
Vol 50 (1) ◽  
pp. 54-63 ◽  
Author(s):  
Keisuke Matsumoto ◽  
Toshio Nakata
Keyword(s):  
Random Walks ◽  
Limit Theorems ◽  
Law Of Large Numbers ◽  
Convergence In Distribution ◽  
Stable Law ◽  
One Dimensional ◽  
Limit Distributions ◽  
Polynomial Size ◽  
Large Numbers ◽  
Geometric Size

In this paper we study limit theorems for the Feller game which is constructed from one-dimensional simple symmetric random walks, and corresponds to the St. Petersburg game. Motivated by a generalization of the St. Petersburg game which was investigated by Gut (2010), we generalize the Feller game by introducing the parameter α. We investigate limit distributions of the generalized Feller game corresponding to the results of Gut. Firstly, we give the weak law of large numbers for α=1. Moreover, for 0<α≤1, we have convergence in distribution to a stable law with index α. Finally, some limit theorems for a polynomial size and a geometric size deviation are given.

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