Stochastic Homogenization on Homogeneous Spaces
نویسنده
چکیده
Motivated by inhomogeneous scaling of left invariant Riemannian metrics on a Lie group G, we consider a family of stochastic differential equations (SDEs) on G with Markov operators L = 1 ∑ k(Ak) 2 + 1 A0 + Y0, where > 0, {Ak} generates a sub Lie-algebra h of the Lie algebra g, and Y0 ∈ g. Assuming that G/H is a reductive homogeneous space, in the sense of Nomizu, we take → 0 and study the asymptotics of the SDEs through the stochastic homoganization problem, and study the effective limit operators on G and on G/H . AMS Mathematics Subject Classification : 60Gxx, 60Hxx, 58J65, 58J70
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