LARGE DEVIATIONS FOR SYMMETRIC DIFFUSION PROCESSES

Let a（x）=(aij（x）) be a uniformly continuous, symmetric and matrix-valued function satisfying uniformly elliptic condition, p（t, x, y） be the transition density function of the diffusion process associated with the Diriehlet space （, H01 （Rd））, where（u, v）=1/2 integral from n=Rd sum from i=j to d(u（x）/xi v（x）/xjaij（x）dx).Then by using the sharpened Arouson’s estimates established by D. W. Stroock, it is shown that2t ln p（t, x, y）=-d2（x, y）.Moreover, it is proved that Py6 has large deviation property with rate functionI（ω）=1/2 integral from n=0 to 1<（t）, α-1（ω（t））,（t）>dtas s→0 and y→x, where Py6 denotes the diffusion measure family associated with the Dirichlet form （ε, H01（Rd））.