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Quasimartingales associated to Markov processes. (English) Zbl 1425.60068

Authors’ abstract: For a fixed right process \(X\) the authors investigate those functions \(u\) for which \(u(X)\) is a quasimartingale. They prove that \(u(X)\) is a quasimartingale if and only if \(u\) is the difference of two finite excessive functions. The study relies on an analytic reformulation of the quasimartingale property for \(u(X)\) in terms of a certain variation of \(u\) with respect to the transition function of the process.

MSC:

60J45 Probabilistic potential theory
31C25 Dirichlet forms
60J40 Right processes
60J25 Continuous-time Markov processes on general state spaces
60J35 Transition functions, generators and resolvents
60J55 Local time and additive functionals
60J57 Multiplicative functionals and Markov processes
31C05 Harmonic, subharmonic, superharmonic functions on other spaces
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