Osterwalder-Schrader (OS) positive symmetric stationary stochastic processes are discussed. A natural construction is given for the associated positive semigroup structure. Conversely, OS-positive symmetric stationary stochastic processes are constructed from positive semigroup structures. OS-positive processes are seen to be the natural generalization of Markov processes, positive semigroup structures being the natural generalization of positivity preserving semigroups. The inheritability of OS-positivity is discussed.
"A Generalization of Markov Processes." Ann. Probab. 6 (1) 128 - 132, February, 1978. https://doi.org/10.1214/aop/1176995616