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Kyeong-Hun Kim

  1. An $L^2$-theory on SPDE driven by L\'evy processes.

    Mon, 07/26/2010 - 15:01 — SomNambul
    Authors: Zhen-Qing Chen, Kyeong-Hun Kim
    Subjects: Probability
    Abstract

    In this paper we develop an $L_2$-theory for stochastic partial differential
    equations driven by L\'evy processes.

    The coefficients of the equations are random functions depending on time and
    space variables, and no smoothness assumption of the coefficients is assumed.

  2. An $L^p$-theory of non-divergence form SPDEs driven by L\'evy processes.

    Wed, 07/21/2010 - 15:01 — SomNambul
    Authors: Zhen-Qing Chen, Kyeong-Hun Kim
    Subjects: Probability
    Abstract

    In this paper we present an $L^p$-theory for the stochastic partial
    differential equations (SPDEs in abbreciation) driven by L\'e{}vy processes.
    Existence and uniqueness of solutions in Sobolev spaces are obtained. The
    coefficients of SPDEs under consideration are random functions depending on
    time and space variables.

  3. A generalization of the Littlewood-Paley inequality for the fractional Laplacian $(-\Delta)^{\alpha/2}$.

    Wed, 06/16/2010 - 15:01 — SomNambul
    Authors: Ildoo Kim, Kyeong-Hun Kim
    Subjects: Functional Analysis
    Abstract

    We prove a parabolic version of the Littlewood-Paley inequality for the
    fractional Laplacian $(-\Delta)^{\alpha/2}$, where $\alpha\in (0,2)$.

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