User:A ringh/sanbox 2

A reciprocal process (also known as Bernstein process ) is a stochastic process...

Another paramount reference in this context.

It is related to the concept of a Markov process; in fact, all Markov processes are reciprocal processes.

Definition
Let $$(A, \mathcal{A})$$ be a measure space, and let $$\{X_t \mid a \leq t \leq b \}$$ be a $$(M, \Sigma)$$-valued stochastic process with underlying probability space $$(B, \mathcal{B}, P)$$. The stochastic process is said to be reciprocal if, for each $$a \leq t_1 < t_2 \leq b $$,


 * $$P(ab \mid X_{t_1}, X_{t_2}) = ... $$