Heat kernels for non-symmetric diffusion operators with jumps

By Zhen-Qing Chen, Eryan Hu, Longjie Xie, Xicheng Zhang. 2016

72 citations recorded by the source corpus.

For $d\geq 2$, we establish the existence and uniqueness of heat kernels for a large class of time-dependent second order diffusion operator with jumps, which is the sum of time-dependent of a second order elliptic differential operators non-divergence form and a non-local $\alpha$-stable-type operator with bounded time-dependent coefficient. Moreover, we obtain sharp two-sided estimates, gradient estimate and fractional derivative estimate for the heat kernels under some mild conditions. Our approach is mainly analytic but also uses some probabilistic techniques.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/2fe01700e235f85d885dc83ade70f4adc0f24085

Citations in the corpus

• Ergodicity of stochastic differential equations with jumps and singular coefficients (2017, unknown): “Under (Hβ), it is well known that L a 2 admits a fundamental solution (also called heat kernel) ρ(s, x; t, y) so that ∂sρ(s, x; t, y) + L a 2 ρ(s, ·; t, y)(x) = 0, lim s↑t ρ(s, x; t, y) = δx−y, and ρ(s, x; t, y) enjoys the following gradient estimates (see [17, Chapter 2] or [11]): |∇ j xρ(s, ·; t, ”