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Stochastic quantization and ergodic theorem for density of diffusions

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Abstract

For a given probability density function ρ(x) on ℝd, we construct a (non-stationary) diffusion process x t , starting at any point x in ℝd, such that \(\frac{1} {T} \)∫ T0 δ x t − x)dt converges to ρ(x) almost surely. The rate of this convergence is also investigated. To find this rate, we mainly use the Clark-Ocone formula from Malliavin calculus and the Girsanov transformation technique.

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  1. Department of Mathematics, University of Kansas, Lawrence, KS, 66045, USA

    YaoZhong Hu

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  1. YaoZhong Hu
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Correspondence to YaoZhong Hu.

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Hu, Y. Stochastic quantization and ergodic theorem for density of diffusions. Sci. China Math. 55, 2285–2296 (2012). https://doi.org/10.1007/s11425-012-4523-7

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  • DOI: https://doi.org/10.1007/s11425-012-4523-7

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