کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6419327 1339394 2012 12 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A new proof of Doobʼs theorem
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
A new proof of Doobʼs theorem
چکیده انگلیسی

We prove that every bounded, positive, irreducible, stochastically continuous semigroup on the space of bounded, measurable functions which is strong Feller, consists of kernel operators and possesses an invariant measure converges pointwise. This differs from Doobʼs theorem in that we do not require the semigroup to be Markovian and request a fairly weak kind of irreducibility. In addition, we elaborate on the various notions of kernel operators in this context, show the stronger result that the adjoint semigroup converges strongly and discuss as an example diffusion equations on rough domains. The proofs are based on the theory of positive semigroups and do not use probability theory.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 388, Issue 2, 15 April 2012, Pages 763-774
نویسندگان
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