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- W4385227492 abstract "Birth and death Markov processes can model stochastic physical systems from percolation to disease spread and, in particular, wildfires. We introduce and analyze a birth-death-suppression Markov process as a model of controlled culling of an abstract, dynamic population. Using analytic techniques, we characterize the probabilities and timescales of outcomes like absorption at zero (extinguishment) and the probability of the cumulative population (burned area) reaching a given size. The latter requires control over the embedded Markov chain: this discrete process is solved using the Pollazcek orthogonal polynomials, a deformation of the Gegenbauer/ultraspherical polynomials. This allows analysis of processes with bounded cumulative population, corresponding to finite burnable substrate in the wildfire interpretation, with probabilities represented as spectral integrals. This technology is developed in order to lay the foundations for a dynamic decision support framework. We devise real-time risk metrics and suggest future directions for determining optimal suppression strategies, including multi-event resource allocation problems and potential applications for reinforcement learning." @default.
- W4385227492 created "2023-07-25" @default.
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- W4385227492 date "2023-07-21" @default.
- W4385227492 modified "2023-10-12" @default.
- W4385227492 title "Birth-death-suppression Markov process and wildfires" @default.
- W4385227492 doi "https://doi.org/10.48550/arxiv.2307.11726" @default.
- W4385227492 hasPublicationYear "2023" @default.
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