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A Necessary Characteristic Equation of Diffusion Processes Having Gaussian Marginals

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  • Syeda Rabab Mudakkar

Abstract

The aim of this work is to characterize one‐dimensional homogeneous diffusion process, under the assumption that marginal density of the process is Gaussian. The method considers the forward Kolmogorov equation and Fourier transform operator approach. The result establishes the necessary characteristic equation between drift and diffusion coefficients for homogeneous and nonhomogeneous diffusion processes. The equation for homogeneous diffusion process leads to characterize the possible diffusion processes that can exist. Two well‐known examples using the necessary characteristic equation are also given.

Suggested Citation

  • Syeda Rabab Mudakkar, 2012. "A Necessary Characteristic Equation of Diffusion Processes Having Gaussian Marginals," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:598590
    DOI: 10.1155/2012/598590
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    References listed on IDEAS

    as
    1. Kais Hamza & Fima C. Klebaner, 2007. "A Family of Non-Gaussian Martingales with Gaussian Marginals," International Journal of Stochastic Analysis, Hindawi, vol. 2007, pages 1-19, August.
    2. Bo Martin Bibby & Michael Sørensen, 2001. "Simplified Estimating Functions for Diffusion Models with a High‐dimensional Parameter," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(1), pages 99-112, March.
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