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A reciprocal process (also known as Bernstein process^[1]) 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.^[2]^{: Lemma 1.2}

Definition edit

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}})=...

^[2]

References edit

^ Christian, Léonard; Rœlly, Sylvie; Zambrini, Jean-Claude (2014). "Reciprocal processes. A measure-theoretical point of view". Probability Surveys. 11: 237–269. doi:10.1214/13-PS220.
^ ^a ^b Jamison, Benton (1974). "Reciprocal processes". Wahrscheinlichkeitstheorie und Verwandte Gebiete. 30 (1): 65–86. doi:10.1007/BF00532864.

[leonard2014-1] Christian, Léonard; Rœlly, Sylvie; Zambrini, Jean-Claude (2014). "Reciprocal processes. A measure-theoretical point of view". Probability Surveys. 11: 237–269. doi:10.1214/13-PS220.

[jamison1974-2] Jamison, Benton (1974). "Reciprocal processes". Wahrscheinlichkeitstheorie und Verwandte Gebiete. 30 (1): 65–86. doi:10.1007/BF00532864.

[1]

[2]