Some heat operators on \(\mathbb{P}(\mathbb{R}^ d)\). (English) Zbl 0874.58091

The authors construct the heat operator on the Wiener space \(\mathbb{P}(\mathbb{R}^n)\) of continuous maps defined on \([0,1]\) with values in \(\mathbb{R}^n\), by taking the sum of the square of twisted derivatives with respect to an orthonormal basis of the Cameron-Martin space of the Wiener space.


58J65 Diffusion processes and stochastic analysis on manifolds
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