A Generalized Stochastic Calculus in Homogenization

  • Masatoshi Fukushima
Conference paper


Take a formally self-adjoint second order partial differential operator with the coefficients aij(x) being periodic in x.

When aij are smooth, Bensoussan-Lions-Papanicolaou showed that the diffusion process corresponding to the coefficients \( {{\text{a}}_{{{\text{ij}}}}}\left( {\frac{{\text{x}}}{\varepsilon }} \right) \) converges as ε ↓ 0 to a diffusion with constant coefficients. We show that their method still works without any smoothness assumption by using a stochastic calculus relevant to the Dirichlet forms.


Harmonic Function Dirichlet Form Additive Functional Stochastic Calculus Finite Energy 
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Copyright information

© Springer-Verlag/Wien 1980

Authors and Affiliations

  • Masatoshi Fukushima
    • 1
  1. 1.Osaka UniversityToyonaka, OsakaJapan

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