On the martingale problem for pseudo-differential operators of variable order
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
On the martingale problem for pseudo-differential operators of variable order
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| Creator |
Komatsu, T.
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| Description |
Consider parabolic pseudo-differential operators L = ∂t − p(x,Dx) of variable order α(x) ≤ 2. The function α(x) is assumed to be smooth, but the symbol p(x, ξ) is not always differentiable with respect to x. We will show the uniqueness of Markov processes with the generator L. The essential point in our study is to obtain the Lp-estimate for resolvent operators associated with solutions to the martingale problem for L. We will show that, by making use of the theory of pseudo-differential operators and a generalized Calderon–Zygmund inequality for singular integrals. As a consequence of our study, the Markov process with the generator L is constructed and characterized. The Markov process may be called a stable-like process with perturbation.
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| Date |
2009-12-03T16:36:19Z
2009-12-03T16:36:19Z 2008 |
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| Type |
Article
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| Identifier |
On the martingale problem for pseudo-differential operators of variable order / T. Komatsu // Theory of Stochastic Processes. — 2008. — Т. 14 (30), № 2. — С. 42–51. — Бібліогр.: 10 назв.— англ.
0321-3900 http://dspace.nbuv.gov.ua/handle/123456789/4551 519.21 |
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| Language |
en
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| Publisher |
Інститут математики НАН України
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