• Title/Summary/Keyword: two-sided Brownian motion

Search Result 4, Processing Time 0.016 seconds

ON ESTIMATES OF POISSON KERNELS FOR SYMMETRIC LÉVY PROCESSES

  • Kang, Jaehoon;Kim, Panki
    • Journal of the Korean Mathematical Society
    • /
    • v.50 no.5
    • /
    • pp.1009-1031
    • /
    • 2013
  • In this paper, using elementary calculus only, we give a simple proof that Green function estimates imply the sharp two-sided pointwise estimates for Poisson kernels for subordinate Brownian motions. In particular, by combining the recent result of Kim and Mimica [5], our result provides the sharp two-sided estimates for Poisson kernels for a large class of subordinate Brownian motions including geometric stable processes.

Nonparametric Discontinuity Point Estimation in Density or Density Derivatives

  • Huh, Jib
    • Journal of the Korean Statistical Society
    • /
    • v.31 no.2
    • /
    • pp.261-276
    • /
    • 2002
  • Probability density or its derivatives may have a discontinuity/change point at an unknown location. We propose a method of estimating the location and the jump size of the discontinuity point based on kernel type density or density derivatives estimators with one-sided equivalent kernels. The rates of convergence of the proposed estimators are derived, and the finite-sample performances of the methods are illustrated by simulated examples.

MULTIDIMENSIONAL SYMMETRIC STABLE PROCESSES

  • Chen, Zhen-Qing
    • Journal of applied mathematics & informatics
    • /
    • v.6 no.2
    • /
    • pp.329-368
    • /
    • 1999
  • This paper surveys recent remarkable progress in the study of potential theory for symmetric stable processes. It also contains new results on the two-sided estimates for Green functions Poisson kernels and Martin kernels of discontinuous symmetric $alpha$ -stable process in bounded $C^{1,1}$ open sets. The new results give ex-plicit information on how the comparing constants depend on pa-rametrer $alpha$ and consequently recover the green function and Poisson kernel estimates for Brownian motion by passing $alpha{\uparrow}2$. In addition to these new estimates this paper surveys recent progress in the study of notions of harmonicity integral representation of harmonic func-tions boundary harnack inequality conditional gauge and intrinsic ultracontractivity for symmetric stable processes. Here is a table of contents.