Asymptotics for certain Wiener integrals associated with higher order differential operators (Q805072)

The large deviation results of Donsker-Varadhan for operators of the form \(\Delta_ x+V(x)\), where \(\Delta_ x\) is the Laplacian and V(x) is a real-valued potential, are extended here to operators of the form \(\Delta_ x+c(x)A_ y\), where c(x) is a non-negative locally Hölder function and \(A_ y\) is a formally selfadjoint elliptic operator of order 2r (operating on functions of y). In particular, the principal eigenvalue for this operator is given as the asymptotic limit of a certain Wiener integral. An application is given to the operator \(\partial^ 2/\partial x^ 2-c(x) \partial^ 4/\partial y^ 4,\) which arises in elasticity theory.