h-transform for Bochner subordinate Lp-semigroups
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2022-09-23 19:09
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LUPAȘCU-STAMATE, Oana. h-transform for Bochner subordinate Lp-semigroups. In: Conference on Applied and Industrial Mathematics: CAIM 2021, 17-18 septembrie 2021, Iași, România. Chișinău, Republica Moldova: Casa Editorial-Poligrafică „Bons Offices”, 2021, Ediţia a 28-a, p. 45.
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Conference on Applied and Industrial Mathematics
Ediţia a 28-a, 2021
Conferința "Conference on Applied and Industrial Mathematics"
Iași, România, Romania, 17-18 septembrie 2021

h-transform for Bochner subordinate Lp-semigroups


Pag. 45-45

Lupașcu-Stamate Oana
 
"Gheorghe Mihoc - Caius Iacob" Institute of Mathematical Statistics and Applied Mathematics of Romanian Academy
 
Disponibil în IBN: 21 septembrie 2022


Rezumat

We show that the subordination induced by a convolution semigroup (subordination in the sense of Bochner) of a C0-semigroup of sub-Markovian operators on an Lp space is actually associated to the subordination of a right (Markov) process. As a consequence, we solve the martingale problem associate with the Lp-in nitesimal generator of the subordinate semigroup. It turns out that an enlargement of the base space is necessary. A main step in the proof is the preservation under such a subordination of the property of a Markov process to be a Borel right process. We also investigate the h-transform of a subordinate C0-semigroup of sub-Markovian operators on an Lp space. The results were obtained jointly with Lucian Beznea and Ana-Maria Boeangiu.