Abstract
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.
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References
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Fukushima, M. (1980). A Generalized Stochastic Calculus in Homogenization. In: Streit, L. (eds) Quantum Fields — Algebras, Processes. Springer, Vienna. https://doi.org/10.1007/978-3-7091-8598-8_3
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DOI: https://doi.org/10.1007/978-3-7091-8598-8_3
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