An eigenvalue decomposition for first hitting times in random walks

1983 ◽  
Vol 63 (1) ◽  
pp. 71-84 ◽  
Author(s):  
John T. Kent ◽  
Nicholas T. Longford
Keyword(s):  
Random Walks ◽  
Eigenvalue Decomposition ◽  
Hitting Times ◽  
First Hitting Times

scholarly journals First hitting times of simple random walks on graphs with congestion points

2003 ◽  
Vol 2003 (30) ◽  
pp. 1911-1922 ◽  
Author(s):  
Mihyun Kang
Keyword(s):  
Random Walks ◽  
Generating Functions ◽  
Hitting Times ◽  
Group Representations ◽  
Explicit Formulas ◽  
Probability Generating Functions ◽  
Random Walks On Graphs ◽  
First Hitting Times

We derive the explicit formulas of the probability generating functions of the first hitting times of simple random walks on graphs with congestion points using group representations.

On a Result of Aleliunas et al. Concerning Random Walks on Graphs

1990 ◽  
Vol 4 (4) ◽  
pp. 489-492 ◽  
Author(s):  
José Luis Palacios
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Simple Proof ◽  
Hitting Times ◽  
Initial State ◽  
Random Walks On Graphs ◽  
Minimum Number

Aleliunas et al. [3] proved that for a random walk on a connected raph G = (V, E) on N vertices, the expected minimum number of steps to visit all vertices is bounded by 2|E|(N - 1), regardless of the initial state. We give here a simple proof of that result through an equality involving hitting times of vertices that can be extended to an inequality for hitting times of edges, thus obtaining a bound for the expected minimum number of steps to visit all edges exactly once in each direction.

scholarly journals First Hitting Times to Intermittent Targets

2019 ◽  
Vol 123 (25) ◽  
Author(s):  
Gabriel Mercado-Vásquez ◽  
Denis Boyer
Keyword(s):  
Hitting Times ◽  
First Hitting Times

Examples for the Theory of Strong Stationary Duality with Countable State Spaces

1990 ◽  
Vol 4 (2) ◽  
pp. 157-180 ◽  
Author(s):  
Persi Diaconis ◽  
James Allen Fill
Keyword(s):  
Stopping Time ◽  
Renewal Theory ◽  
Hitting Times ◽  
State Spaces ◽  
Ergodic Markov Chain ◽  
Countable State Space ◽  
Strong Stationary Duality ◽  
Countable State ◽  
Infinite State ◽  
First Hitting Times

Let X1,X2,… be an ergodic Markov chain on the countable state space. We construct a strong stationary dual chain X* whose first hitting times give sharp bounds on the convergence to stationarity for X. Examples include birth and death chains, queueing models, and the excess life process of renewal theory. This paper gives the first extension of the stopping time arguments of Aldous and Diaconis [1,2] to infinite state spaces.

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