Abstract.
This work is concerned with existence for a stochastic free boundary problem arising in phase transition (the Stefan two phase problem). The existence of an invariant ergodic measure associated with the corresponding transition semigroup P(t) is also proved, together with an integration by parts formula for the generator of P(t).
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Received: 20 June 2001 / Revised version: 17 June 2002 / Published online: 24 October 2002
Mathematics Subject Classification (2000): 35K35, 35R15, 60H15
Key words or phrases: Stochastic Stefan problem – Invariant measures – Wiener process – Transition semigroup – Kolmogorov operator
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Barbu, V., Da Prato, G. The two phase stochastic Stefan problem. Probab Theory Relat Fields 124, 544–560 (2002). https://doi.org/10.1007/s00440-002-0232-4
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DOI: https://doi.org/10.1007/s00440-002-0232-4