Abels, Helmut and Kassmann, Moritz (2009) THE CAUCHY PROBLEM AND THE MARTINGALE PROBLEM FOR INTEGRO-DIFFERENTIAL OPERATORS WITH NON-SMOOTH KERNELS. OSAKA JOURNAL OF MATHEMATICS, 46 (3). pp. 661-683. ISSN 0030-6126,
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We consider the linear integro-differential operator L defined by Lu(x) = integral(Rn) (u(x + y) - u(x) - 1([1,2])(alpha)1([vertical bar y vertical bar <= 2])(y)y. del u(x))k(x, y)dy. Here the kernel k(x, y) behaves like vertical bar y vertical bar(-n-alpha), alpha is an element of (0, 2), for small y and is Holdercontinuous in the first variable, precise definitions are given below. We study the unique solvability of the Cauchy problem corresponding to L. As an application we obtain well-posedness of the martingale problem for L. Our strategy follows the classical path of Stroock-Varadhan. The assumptions allow for cases that have not been dealt with so far.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | H-INFINITY-CALCULUS; PSEUDODIFFERENTIAL-OPERATORS; VARIABLE ORDER; MARKOV-PROCESSES; GENERATORS; UNIQUENESS; EQUATIONS; SYMBOLS; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Helmut Abels |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 09 Sep 2020 06:58 |
| Last Modified: | 09 Sep 2020 06:58 |
| URI: | https://pred.uni-regensburg.de/id/eprint/28527 |
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