| Abstract: |
| In this talk, we will give the existence of martingale solutions to the stochastic heat equation with spatial variable on
the whole line and taking values in a non-compact Riemannian manifold, which admits Wiener measure as an invariant measure by using Dirichlet form. Moreover, we establish the log-Sobolev inequality when Ricci curvature is strictly positive which implies exponential ergodicity for the process. Also when the sectional curvature is negative, the process is non-ergodic. |
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