Abstract.
We study the weak duality between two sub-Markovian resolvents of kernels on a Lusin topological space with respect to a given measure m. Our frame covers the probabilistic context of two Borel Markov processes in weak duality. The main results are related to: the coincidence of the m-semipolar and m-cosemipolar sets, the Revuz correspondence between the measures charging no cofinely open m-polar set and the potential kernels associated with the homogeneous random measures of the process, the equivalence between smoothness and cosmoothness (a smooth measure is the Revuz measure of a continuous additive functional). We extend and improve results of R.M. Blumenthal-R.K. Getoor, J. Azéma, D. Revuz, J.B. Walsh, R.K. Getoor-M.J. Sharpe.
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Received: 24 July 2001 / Revised version: 29 December 2002 / Published online: 12 May 2003
Supported by the CNCSIS grant no. 33518/2002 (code 431), the CERES program of the Romanian Ministry of Ed. and Research, contract no. 152/2001 and the EURROMMAT program ICA1-CT-2000-70022 of the European Commission.
Mathematics Subject Classification (2000): 60J40, 60J45, 60J55, 60J35, 31C15, 31C25, 31D05
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Beznea, L., Boboc, N. Sub-Markovian resolvents under weak duality hypothesis. Probab. Theory Relat. Fields 126, 339–363 (2003). https://doi.org/10.1007/s00440-003-0255-5
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DOI: https://doi.org/10.1007/s00440-003-0255-5
Keywords
- Topological Space
- Markov Process
- Random Measure
- Weak Duality
- Smooth Measure