On the martingale problem for pseudo-differential operators of variable order

• Date: 2008
• ISSN: 0321-3900
• Main Author: Komatsu, T.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2008
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/4551
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: 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.

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...