TL;DR
This paper introduces Fibonacci matrices to analyze a one-dimensional random walk with varying transition probabilities, providing new formulas for expected arrivals and absorption times.
Contribution
It presents a novel application of Fibonacci matrices to compute key metrics in a complex random walk model.
Findings
Derived formulas for expected number of arrivals
Calculated expected absorption times
Demonstrated effectiveness of Fibonacci matrices in stochastic analysis
Abstract
We study a discrete random walk on a one-dimensional finite lattice, where each state has different probabilities to move one step forward, backward, staying for a moment or being absorbed. We obtain expected number of arrivals and expected time until absorption using a new concept: Fibonacci matrices.
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Taxonomy
TopicsStochastic processes and statistical mechanics · DNA and Biological Computing