• Title, Summary, Keyword: ergodic diffusion processes

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Minimum Density Power Divergence Estimator for Diffusion Parameter in Discretely Observed Diffusion Processes

  • Song, Jun-Mo;Lee, Sang-Yeol;Na, Ok-Young;Kim, Hyo-Jung
    • Communications for Statistical Applications and Methods
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    • v.14 no.2
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    • pp.267-280
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    • 2007
  • In this paper, we consider the robust estimation for diffusion processes when the sample is observed discretely. As a robust estimator, we consider the minimizing density power divergence estimator (MDPDE) proposed by Basu et al. (1998). It is shown that the MDPDE for diffusion process is weakly consistent. A simulation study demonstrates the robustness of the MDPDE.

ON THE DIFFUSION OPERATOR IN POPULATION GENETICS

  • Choi, Won
    • Journal of applied mathematics & informatics
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    • v.30 no.3_4
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    • pp.677-683
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    • 2012
  • W.Choi([1]) obtains a complete description of ergodic property and several property by making use of the semigroup method. In this note, we shall consider separately the martingale problems for two operators A and B as a detail decomposition of operator L. A key point is that the (K, L, $p$)-martingale problem in population genetics model is related to diffusion processes, so we begin with some a priori estimates and we shall show existence of contraction semigroup {$T_t$} associated with decomposition operator A.

Continuous Time Approximations to GARCH(1, 1)-Family Models and Their Limiting Properties

  • Lee, O.
    • Communications for Statistical Applications and Methods
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    • v.21 no.4
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    • pp.327-334
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    • 2014
  • Various modified GARCH(1, 1) models have been found adequate in many applications. We are interested in their continuous time versions and limiting properties. We first define a stochastic integral that includes useful continuous time versions of modified GARCH(1, 1) processes and give sufficient conditions under which the process is exponentially ergodic and ${\beta}$-mixing. The central limit theorem for the process is also obtained.