In this study, we consider general Markov chains (MC) defined by a transition probability (kernel) that is finitely additive. These were constructed S. Ramakrishnan within the concepts and symbolism of game theory. Here, study these MCs using operator approach. our work, state space (phase space) MC has any cardinality sigma-algebra discrete. The construction phase allows us to decompose kernel...

The recent study by B. De Bruyne, S. N. Majumdar, H. Orland and G. Schehr [arXiv:2110.07573], concerning the conditioning of Brownian motion random walks on global dynamical constraints over a finite time-window $T$, is reformulated as general framework for 'microcanonical conditioning' Markov processes time-additive observables. This formalism applied to various types processes, namely discret...