Hybrid discrete/continuum forward and backward operators, with applications to large-population extinction time problems

PeterThomas

Case Western Reserve University

"Hybrid discrete/continuum forward and backward operators, with applications to large-population extinction time problems"

Safta et al (J.~Comp.~Phys. 2015) introduced a hybrid discrete/continuous representation of Kolmogorov's forward operator, $mathcal{L}$, for numerically simulating the evolution of probability distributions on state spaces spanning both large and small numbers of molecules. Motivated by first-passage-time (e.g. extinction time) and exit-distribution problems, we extend Safta et al's approach to establish a hybrid discrete/continuum representation of Kolmogorov's backward operator $mathcal{L}^dagger$, the formal adjoint of $mathcal{L}$ also known as the Markov process generator, or the stochastic Koopman operator. We apply our coarsened backward operators to several birth-death processes of increasing complexity, leveraging exact results where available to evaluate their speed and accuracy.
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