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Aldous and Pitman have a paper on "Brownian bridge asymptotics for random mappings", which describes a setting in which Brownian bridge shows up as a limit object and is most naturally thought of as i …

The proof by Barsky et. al. that there is no percolation in half-spaces proceeds by a dynamic renormalization argument. The proof couples critical percolation in the half-space $\mathbb{H}^d$ with a d …

I think the right way to phrase this discussion is as follows. Let $(X_s)_{0 \leq s \leq t}$ be a real stochastic process with cyclically exchangeable increments: for all $u \in [0,t]$, the process $( …

Based on the comments to this answer, I no longer believe what I initially wrote (still appearing at the bottom of the answer). It seems to me a construction should be possible. It is at least possibl …

In general, if $M$ was the transition matrix (infinitesimal generator) of a Markov chain , this functional would be called called the resolvent. Perhaps you already knew this; if not, you could look a …

This kind of question is an active area of research. I don't think the answer to your question is known, but here are the two most closely-related bits of research I'm aware of. (1) A Poisson hard-s …

Let $(m_i, i \in \mathbb{N})$ be positive weights with $\sum_{i \in \mathbb{N}} m_i^2 < 0.1$. Consider a subcritical branching process in discrete time and continuous space, started from some initial …