Bound for an Approximation of Invariant Density of Diffusions via Density Formula in Malliavin Calculus

Yoon-Tae Kim and Hyun-Suk Park ()
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Yoon-Tae Kim: Division of Data Science and Data Science Convergence Research Center, Hallym University, Chuncheon 24252, Republic of Korea
Hyun-Suk Park: Division of Data Science and Data Science Convergence Research Center, Hallym University, Chuncheon 24252, Republic of Korea

Mathematics, 2023, vol. 11, issue 10, 1-18

Abstract: The Kolmogorov and total variation distance between the laws of random variables have upper bounds represented by the L 1 -norm of densities when random variables have densities. In this paper, we derive an upper bound, in terms of densities such as the Kolmogorov and total variation distance, for several probabilistic distances (e.g., Kolmogorov distance, total variation distance, Wasserstein distance, Forter–Mourier distance, etc.) between the laws of F and G in the case where a random variable F follows the invariant measure that admits a density and a differentiable random variable G , in the sense of Malliavin calculus, and also allows a density function.

Keywords: Malliavin calculus; invariant measure; density function; Stein’s bound; fourth moment theorem; probabilistic distance; Scheffe’s theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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