Markov processes form a fundamental class of stochastic models in which the evolution of a system is delineated by the memoryless property. In such processes, the future state depends solely on the ...

Let $X = (X_t, P^x)$ be a right Markov process and let $m$ be an excessive measure for $X$. Associated with the pair $(X, m)$ is a stationary strong Markov process ...

We study the evolution of a particle system whose genealogy is given by a supercritical continuous time Galton-Watson tree. The particles move independently according to a Markov process and when a ...

A new framework for generative diffusion models was developed by researchers at Science Tokyo, significantly improving ...