CONVERGENCE IN WASSERSTEIN DISTANCE FOR EMPIRICAL MEASURES OF SEMILINEAR SPDES

被引：3

作者：

Wang, Feng-Yu ^{[1
]}

机构：

[1] Tianjin Univ, Ctr Appl Math, Tianjin, Peoples R China

来源：

ANNALS OF APPLIED PROBABILITY | 2023年 / 33卷 / 01期

关键词：

Wasserstein distance; empirical measure; semilinear SPDE; convergence rate;

D O I：

10.1214/22-AAP1807

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

The convergence rate in Wasserstein distance is estimated for the em-pirical measures of symmetric semilinear SPDEs. Unlike in the finite -dimensional case that the convergence is of algebraic order in time, in the present situation the convergence is of log order with a power given by eigen-values of the underlying linear operator.

引用

页码：70 / 84

页数：15

共 50 条

[21] Limit theorems in Wasserstein distance for empirical measures of diffusion processes on Riemannian manifolds
Wang, Feng-Yu
Zhu, Jie-Xiang
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2023, 59 (01): : 437 - 475
[22] Reconstructing discrete measures from projections. Consequences on the empirical Sliced Wasserstein Distance
Tanguy, Eloi
Flamary, Remi
Delon, Julie
COMPTES RENDUS MATHEMATIQUE, 2024, 362
[23] Derivative formula and exponential convergence for semilinear SPDEs driven by Levy processes
Song, Yulin
STATISTICS & PROBABILITY LETTERS, 2014, 89 : 99 - 109
[24] CONVERGENCE OF THE EMPIRICAL MEASURE IN EXPECTED WASSERSTEIN DISTANCE: NON-ASYMPTOTIC EXPLICIT BOUNDS IN Rd
Fournier, Nicolas
ESAIM-PROBABILITY AND STATISTICS, 2023, 27 : 749 - 775
[25] On the Wasserstein distance between mutually singular measures
Buttazzo, Giuseppe
Carlier, Guillaume
Laborde, Maxime
ADVANCES IN CALCULUS OF VARIATIONS, 2020, 13 (02) : 141 - 154
[26] Concentration of risk measures: A Wasserstein distance approach
Bhat, Sanjay P.
Prashanth, L. A.
ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 32 (NIPS 2019), 2019, 32
[27] Generalized Wasserstein Distance and Weak Convergence of Sublinear Expectations
Xinpeng Li
Yiqing Lin
Journal of Theoretical Probability, 2017, 30 : 581 - 593
[28] Subgeometric rates of convergence in Wasserstein distance for Markov chains
Durmus, Alain
Fort, Gersende
Moulines, Eric
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2016, 52 (04): : 1799 - 1822
[29] Generalized Wasserstein Distance and Weak Convergence of Sublinear Expectations
Li, Xinpeng
Lin, Yiqing
JOURNAL OF THEORETICAL PROBABILITY, 2017, 30 (02) : 581 - 593
[30] Non-monotone Convergence in the Quadratic Wasserstein Distance
Schachermayer, Walter
Schmock, Uwe
Teichmann, Josef
SEMINAIRE DE PROBABILITES XLII, 2009, 1979 : 131 - 136

← 1 2 3 4 5 →