I. Cîmpean

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math.PR2019

A natural extension of Markov processes and applications to singular SDEs

Lucian Beznea, Iulian Cîmpean, Michael Röckner

We develop a general method for extending Markov processes to a larger state space such that the added points form a polar set. The so obtained extension is an improvement on the s…

math.PR2017

Invariant, super and quasi-martingale functions of a Markov process

Iulian Cîmpean, Lucian Beznea

We identify the linear space spanned by the real-valued excessive functions of a Markov process with the set of those functions which are quasimartingales when we compose them with…

math.PR2017

Quasimartingales associated to Markov processes

Lucian Beznea, Iulian Cîmpean

For a fixed right process $X$ we investigate those functions $u$ for which $u (X)$ is a quasimartingale. We prove that $u (X)$ is a quasimartingale if and only if $u$ is the dif- fer…