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Although diffusion models now occupy a central place in generative modeling, introductory treatments commonly assume Euclidean data and seldom clarify their connection to discrete-state analogues. This article is a self-contained primer on…

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Markov branching systems form a fundamental class of stochastic models that are extensively applied in biology, physics, finance, and other domains. These systems are distinguished by their continuous-time evolution and inherent branching…

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The standard engineering approach to modelling of complex systems is highly compositional. In order to be able to understand (or to control) the behavior of a complex dynamical systems, it is often desirable, if not necessary, to view this…

The study of first passage times for diffusing particles reaching target states is foundational in various practical applications, including diffusion-controlled reactions. In this work, we present a bi-scaling theory for the probability…

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