## 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.

### MSC:

 58J65 Diffusion processes and stochastic analysis on manifolds
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### References:

 [1] Airault, H., Projection of the infinitesimal generator of a diffusion., J. of Funct. Anal., Vol.85, Aug., 2, (1989). · Zbl 0683.60055 [2] Airault, H. and Malliavin, P. ., Integration on loop groups II., J. of Funct. Anal., Vol.104, Feb. 15, 1, (1992). · Zbl 0787.22021 [3] Airault, H. and Malliavin, P. ., Integration by parts formulas and dilatation vector fields on elliptic probability spaces., To appearProba Theor. and Rel. Fields. · Zbl 0867.60031 [4] Bismut, J.M. ., Large deviations and the Malliavin calculus., Progress in Math. Vol45. Birkhauser; (1984). · Zbl 0537.35003 [5] Fang, S. and Malliavin, P. ., Stochastic Analysis on the path space of a Riemannian manifold., J. of Funct. Anal. Vol.118 , Nov. 15, 1, (1983). · Zbl 0798.58080
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