# The computation of the mean first passage times for Markov chains

@article{Hunter2018TheCO, title={The computation of the mean first passage times for Markov chains}, author={Jeffrey J. Hunter}, journal={Linear Algebra and its Applications}, year={2018} }

Abstract A survey of a variety of computational procedures for finding the mean first passage times in Markov chains is presented. The author recently developed a new accurate computational technique, an Extended GTH Procedure, Hunter (2016) [17] similar to that developed by Kohlas (1986) [20] . In addition, the author recently developed a variety of new perturbation techniques for finding key properties of Markov chains including finding the mean first passage times, Hunter (2016) [18] . These… Expand

#### 17 Citations

Linear Least Square Method for the Computation of the Mean First Passage Times of Ergodic Markov Chains

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- Journal of Advances in Mathematics and Computer Science
- 2018

An efficient and accurate iterative scheme for the computation of the mean first passage times (MFPTs) of ergodic Markov chains has been presented. Firstly, the computation problem of MFPTs is… Expand

Numerical analysis of first-passage processes in finite Markov chains exhibiting metastability.

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- Physical review. E
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All properties required to analyze the first-passage path ensemble (FPPE) at both a microscopic and macroscopic level of detail can be computed using state-reduction methods, and the reactive visitation probability provides a rigorous metric to quantify the dynamical importance of a node for the productive transition between two endpoint states. Expand

Nearly reducible finite Markov chains: Theory and algorithms.

- Medicine
- The Journal of chemical physics
- 2021

All of the information required to determine the kinetically relevant transition mechanisms, and to identify the states that have a dominant effect on the global dynamics, can be computed reliably even for computationally challenging models. Expand

On State Occupancies, First Passage Times and Duration in Non-Homogeneous Semi-Markov Chains

- Mathematics
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- 2021

Semi-Markov processes generalize the Markov chains framework by utilizing abstract sojourn time distributions. They are widely known for offering enhanced accuracy in modeling stochastic phenomena.… Expand

GTH Algorithm, Censored Markov Chains, and $RG$-Factorization

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- 2021

In this paper, we provide a review on the GTH algorithm, which is a numerically stable algorithm for computing stationary probabilities of a Markov chain. Mathematically the GTH algorithm is an… Expand

Performance and stability of direct methods for computing generalized inverses of the graph Laplacian

- Mathematics
- 2020

We consider the computation of generalized inverses of the graph Laplacian for both undirected and directed graphs, with a focus on the group inverse and the closely related absorption inverse. These… Expand

Aggregation of Markov flows I: theory

- Mathematics, Medicine
- Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2018

The main contribution of the paper is to present an alternative, namely a method to aggregate groups of nodes to produce a factor, which can be iterated to make hierarchical aggregation schemes. Expand

HIGH-ORDER MULTIVARIATE MARKOV CHAIN APPLIED IN DOW JONES AND IBOVESPA INDEXES

- Economics
- Pesquisa Operacional
- 2019

In this paper we analyzed the probabilities of transitions of state between Ibovespa and Dow Jones indexes using High-order Multivariate Markov Chain. While the stock market may be profitable, the… Expand

Analysis, Modeling, and Control of Dynamic Processes in Networks

- Computer Science
- 2018

This thesis proposes an algorithm that nullifies the effect of external attacks on the opinion formation process in social networks by strategically recommending a small number of new edges to the network's users by providing a pseudo-linear time heuristic drawn upon the theory of Markov chains. Expand

Reachable Space Characterization of Markov Decision Processes with Time Variability

- Computer Science
- Robotics: Science and Systems
- 2019

The time variability property of the planning stochasticity is explored and the state reachability is investigated, and an efficient iterative method is developed that offers a good trade-off between solution optimality and time complexity. Expand

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