期刊
JOURNAL OF DIFFERENTIAL EQUATIONS
卷 362, 期 -, 页码 266-313出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2023.03.007
关键词
Stable -like processes; Supercritical; Martingale problem; Pathwise uniqueness; Krylov?s estimate; Zvonkin?s; transform
类别
This paper investigates a time-dependent stable-like operator with drift and establishes the well-posedness for the martingale problem associated with it using the Littlewood-Paley theory. It also studies a class of stochastic differential equations driven by generators of the form L-t and proves the pathwise uniqueness of strong solutions for coefficients in certain Besov spaces.
Consider the following time-dependent stable-like operator with drift: -L-t phi(x) = integral(Rd) [phi (x +z) - phi (x ) - z((alpha)) center dot del phi(x)]sigma (t, x, z)nu(alpha)(dz) +b(t, x) center dot del phi(x), where d >= 1, nu(alpha) is an alpha-stable type Levy measure with alpha is an element of (0, 1] and z((alpha)) = 1(alpha)=1(1)|z|<= 1(z), sigma is a real -valued Borel function on R+ x Rd x Rd and b is an Rd-valued Borel function on R+ Chi R-d. By using the Littlewood-Paley theory, we establish the well-posedness for the martingale problem associated with L-t under the sharp balance condition alpha + beta >= 1, where beta is the Holder index of b with respect to x. Moreover, we also study a class of stochastic differential equations driven by Markov processes with generators of the form L-t. We prove the pathwise uniqueness of strong solutions for such equations when the coefficients are in certain Besov spaces.
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