A quantization of diffusion processes on manifolds


Via the well known chaos decomposition with respect to the multidimensional Brownian motion, we give a possible quantization of a diffusion process (in particular, Brownian motion) on a Riemannian manifold. The quantized diffusion process on Riemannian manifold is a quantum Brownian motion on a Holbert space determined by the momentum algebra.

DOI Code: 10.1285/i15900932v14n1p57

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