分野別セミナー

Abstract:
The parametrix method for SDEs driven by one-dimensional stable noises will be discussed, with the special attention payed for two-sided estimates for the transition probability densities. The method is applicable for non-symmetric noises and for the supercritical case of the stability index \alpha<1 and non-trivial drift coefficient, and can be extended to stable-like noses (tempered stable, etc.) Within this method, sensitivities w.r.t. time variable and external parameters are well computable, which has applications in the asymptotic statistics (LAN property for discretely observed Levy driven SDE) and stochastic approximation (rates of approximation for integral functionals of the process with irregular kernels).