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On estimating the derivatives of symmetric diffusions in stationary random environment, with applications to \(\nabla\varphi\) interface model. (English) Zbl 1083.60082
For annealed kernels of diffusions in \({\mathbb R}^d\) or random walks in \({\mathbb Z}^d\), considered in a random environment, the authors show existence and Hölder continuity of second space derivatives and time derivatives. Estimates for these derivatives are also provided. The estimates are applied to the Ginzburg-Landau \(\nabla\varphi\) interface model.

MSC:
60K37 Processes in random environments
60J60 Diffusion processes
60J75 Jump processes (MSC2010)
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