The study of Dirichlet forms and Markov processes in fractal geometry offers a robust framework for analysing irregular spaces that do not conform to classical Euclidean structures. Dirichlet forms ...

We extend the forward-backward martingale approach to Stratonovich integrals developed by Zheng and Lyons to the general context of Dirichlet spaces. From this perspective, it is clear that the ...

We develop a general framework on Dirichlet spaces to prove a weak form of the Bakry-Émery estimate and study its consequences. This estimate may be satisfied in situations, like metric graphs, where ...