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When investigating loops in Markov chains I ran into the following observation. A cycle in a graph $G$ with $n$ vertices may be represented by a matrix $\Gamma \in \mathbb R^{n \times n}$ having the …

Let $0 < c < 1$. Consider the Markov chain $(X_i)$ on $\{0, 1, \dots, n\}$, with transition probabilities $$ P(k,k+1) = \left(1 - \tfrac {k}{n} \right)(1-c), \quad k = 0, \dots, n-1, $$ $$ P(k,k-1) …

Suppose $P(x,dy)$ and $Q(x,dy)$ are two Markov transition kernels on a topological space $E$ equipped with Borel $\sigma$-algebra $\mathcal B(E)$. Suppose for every $x \in E$, $P(x,\cdot)$ and $Q(x, \ …

As only a partial answer, in the paper Bierkens, Roberts, A piecewise deterministic scaling limit of Lifted Metropolis Hastings for the Curie-Weiss model, http://arxiv.org/abs/1509.00302, we have obta …

This question is related to the topic of stochastic filtering theory. See e.g. the following monographs * Bucy, Joseph - Filtering for stochastic processes with applications to guidance * Bain, Crisan …