|
1
|
Lacker D, Yeung LC. A characterization of transportation-information inequalities for Markov processes in terms of dimension-free concentration. ANNALES DE L'INSTITUT HENRI POINCARÉ, PROBABILITÉS ET STATISTIQUES 2023. [DOI: 10.1214/22-aihp1249] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/18/2023]
Affiliation(s)
- Daniel Lacker
- Department of Industrial Engineering & Operations Research, Columbia University, 500 W 120th St, New York, NY 10027, USA
| | - Lane Chun Yeung
- Department of Industrial Engineering & Operations Research, Columbia University, 500 W 120th St, New York, NY 10027, USA
| |
Collapse
|
|
2
|
Strict Kantorovich contractions for Markov chains and Euler schemes with general noise. Stoch Process Their Appl 2022. [DOI: 10.1016/j.spa.2022.06.011] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
|
|
3
|
|
|
4
|
Monmarché P. High-dimensional MCMC with a standard splitting scheme for the underdamped Langevin diffusion. Electron J Stat 2021. [DOI: 10.1214/21-ejs1888] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
|
5
|
Torrisi GL. Concentration inequalities for stochastic differential equations of pure non-Poissonian jumps. Stoch Process Their Appl 2020. [DOI: 10.1016/j.spa.2020.05.017] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
|
|
6
|
Majka MB, Mijatović A, Szpruch Ł. Nonasymptotic bounds for sampling algorithms without log-concavity. ANN APPL PROBAB 2020. [DOI: 10.1214/19-aap1535] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
|
7
|
Adaptive estimation of the stationary density of a stochastic differential equation driven by a fractional Brownian motion. STATISTICAL INFERENCE FOR STOCHASTIC PROCESSES 2020. [DOI: 10.1007/s11203-020-09218-0] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
|
|
8
|
Wang NY, Wu L. Transport-information inequalities for Markov chains. ANN APPL PROBAB 2020. [DOI: 10.1214/19-aap1530] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
|
9
|
Villemonais D. Lower Bound for the Coarse Ricci Curvature of Continuous-Time Pure-Jump Processes. J THEOR PROBAB 2020. [DOI: 10.1007/s10959-019-00918-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
|
|
10
|
Talagrand’s quadratic transportation cost inequalities for reflected SPDEs driven by space–time white noise. Stat Probab Lett 2020. [DOI: 10.1016/j.spl.2020.108734] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
|
|
11
|
Bartl D, Tangpi L. Functional inequalities for forward and backward diffusions. ELECTRON J PROBAB 2020. [DOI: 10.1214/20-ejp495] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
|
12
|
|
|
13
|
Delarue F, Lacker D, Ramanan K. From the master equation to mean field game limit theory: Large deviations and concentration of measure. ANN PROBAB 2020. [DOI: 10.1214/19-aop1359] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
|
14
|
Bahlali K, Boufoussi B, Mouchtabih S. Transportation cost inequality for backward stochastic differential equations. Stat Probab Lett 2019. [DOI: 10.1016/j.spl.2019.108586] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
|
|
15
|
Majka MB. Transportation inequalities for non-globally dissipative SDEs with jumps via Malliavin calculus and coupling. ANNALES DE L'INSTITUT HENRI POINCARÉ, PROBABILITÉS ET STATISTIQUES 2019. [DOI: 10.1214/18-aihp941] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
|
16
|
Shang S, Zhang T. Talagrand concentration inequalities for stochastic heat-type equations under uniform distance. ELECTRON J PROBAB 2019. [DOI: 10.1214/19-ejp388] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
|
17
|
Pal S, Sarantsev A. A note on transportation cost inequalities for diffusions with reflections. ELECTRONIC COMMUNICATIONS IN PROBABILITY 2019. [DOI: 10.1214/19-ecp223] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
|
18
|
Varvenne M. Concentration inequalities for Stochastic Differential Equations with additive fractional noise. ELECTRON J PROBAB 2019. [DOI: 10.1214/19-ejp384] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
|
19
|
Gozlan N, Roberto C, Samson PM, Shu Y, Tetali P. Characterization of a class of weak transport-entropy inequalities on the line. ANNALES DE L'INSTITUT HENRI POINCARÉ, PROBABILITÉS ET STATISTIQUES 2018. [DOI: 10.1214/17-aihp851] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
|
20
|
|
|
21
|
Bitseki Penda SV, Escobar-Bach M, Guillin A. Transportation and concentration inequalities for bifurcating Markov chains. BERNOULLI 2017. [DOI: 10.3150/16-bej843] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
|
22
|
Fontbona J, Gozlan N, Jabir JF. A variational approach to some transport inequalities. ANNALES DE L'INSTITUT HENRI POINCARÉ, PROBABILITÉS ET STATISTIQUES 2017. [DOI: 10.1214/16-aihp769] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
|
23
|
Riedel S. Transportation–cost inequalities for diffusions driven by Gaussian processes. ELECTRON J PROBAB 2017. [DOI: 10.1214/17-ejp40] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
|
24
|
Wintenberger O. Exponential inequalities for unbounded functions of geometrically ergodic Markov chains: applications to quantitative error bounds for regenerative Metropolis algorithms. STATISTICS-ABINGDON 2016. [DOI: 10.1080/02331888.2016.1268205] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Olivier Wintenberger
- LSTA, Sorbonne Universités, Paris, France
- Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark
| |
Collapse
|
|
25
|
A new characterization of quadratic transportation-information inequalities. Probab Theory Relat Fields 2016. [DOI: 10.1007/s00440-016-0721-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
|
|
26
|
|
|
27
|
Paulin D. Concentration inequalities for Markov chains by Marton couplings and spectral methods. ELECTRON J PROBAB 2015. [DOI: 10.1214/ejp.v20-4039] [Citation(s) in RCA: 53] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
|
28
|
Bobkov S, Ding Y. Optimal transport and Rényi informational divergence. ELECTRONIC COMMUNICATIONS IN PROBABILITY 2015. [DOI: 10.1214/ecp.v20-3431] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
|
29
|
Dedecker J, Fan X. Deviation inequalities for separately Lipschitz functionals of iterated random functions. Stoch Process Their Appl 2015. [DOI: 10.1016/j.spa.2014.08.001] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
|
|
30
|
Liu Y. Gaussian integrability of distance function under the Lyapunov
condition. ELECTRONIC COMMUNICATIONS IN PROBABILITY 2015. [DOI: 10.1214/ecp.v20-3838] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
|
31
|
Wang NY, Wu L. Convergence rate and concentration inequalities for Gibbs sampling in high dimension. BERNOULLI 2014. [DOI: 10.3150/13-bej537] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
|
32
|
|
|
33
|
Fournier N, Guillin A. On the rate of convergence in Wasserstein distance of the empirical measure. Probab Theory Relat Fields 2014. [DOI: 10.1007/s00440-014-0583-7] [Citation(s) in RCA: 273] [Impact Index Per Article: 27.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
|
|
34
|
Kontorovich A, Brockwell A. A Strong Law of Large Numbers for Strongly Mixing Processes. COMMUN STAT-THEOR M 2014. [DOI: 10.1080/03610926.2012.701696] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
|
|
35
|
Pal S, Shkolnikov M. Concentration of measure for Brownian particle systems interacting through their ranks. ANN APPL PROBAB 2014. [DOI: 10.1214/13-aap954] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
|
36
|
Boissard E, Le Gouic T. On the mean speed of convergence of empirical and occupation measures in Wasserstein distance. ANNALES DE L'INSTITUT HENRI POINCARÉ, PROBABILITÉS ET STATISTIQUES 2014. [DOI: 10.1214/12-aihp517] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
|
37
|
Bitseki Penda SV, Djellout H, Guillin A. Deviation inequalities, moderate deviations and some limit theorems for bifurcating Markov chains with application. ANN APPL PROBAB 2014. [DOI: 10.1214/13-aap921] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
|
38
|
Paulin D. The convex distance inequality for dependent random variables, with applications to the stochastic travelling salesman and other problems. ELECTRON J PROBAB 2014. [DOI: 10.1214/ejp.v19-3261] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
|
39
|
Wang NY. Concentration inequalities for Gibbs sampling under
$d_{l_{2}}$-metric. ELECTRONIC COMMUNICATIONS IN PROBABILITY 2014. [DOI: 10.1214/ecp.v19-3502] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
|
40
|
Gao F, Guillin A, Wu L. Bernstein-type Concentration Inequalities for Symmetric Markov Processes. THEORY OF PROBABILITY AND ITS APPLICATIONS 2014. [DOI: 10.1137/s0040585x97986667] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
|
|
41
|
Maïda M, Maurel-Segala É. Free transport-entropy inequalities for non-convex potentials and application to concentration for random matrices. Probab Theory Relat Fields 2013. [DOI: 10.1007/s00440-013-0508-x] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
|
|
42
|
Fathi M, Frikha N. Transport-Entropy inequalities and deviation estimates for stochastic approximation schemes. ELECTRON J PROBAB 2013. [DOI: 10.1214/ejp.v18-2586] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
|
43
|
Saussereau B. Transportation inequalities for stochastic differential equations driven by a fractional Brownian motion. BERNOULLI 2012. [DOI: 10.3150/10-bej324] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
|
44
|
Ding Y, Zhang X. A new kind of modified transportation cost inequalities and polynomial concentration inequalities. Stat Probab Lett 2011. [DOI: 10.1016/j.spl.2011.05.006] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
|
|
45
|
Pal S. Concentration for multidimensional diffusions and their boundary local times. Probab Theory Relat Fields 2011. [DOI: 10.1007/s00440-011-0368-1] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
|
|
46
|
Ma Y, Shen S, Wang X, Wu L. Transportation inequalities: From Poisson to Gibbs measures. BERNOULLI 2011. [DOI: 10.3150/00-bej268] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
|
47
|
Boissard E. Simple Bounds for the Convergence of Empirical and Occupation Measures in 1-Wasserstein Distance. ELECTRON J PROBAB 2011. [DOI: 10.1214/ejp.v16-958] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
|
48
|
Milman E. Properties of isoperimetric, functional and Transport-Entropy inequalities via concentration. Probab Theory Relat Fields 2010. [DOI: 10.1007/s00440-010-0328-1] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
|
|
49
|
Joulin A, Ollivier Y. Curvature, concentration and error estimates for Markov chain Monte Carlo. ANN PROBAB 2010. [DOI: 10.1214/10-aop541] [Citation(s) in RCA: 62] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
|
50
|
Bolley F. Quantitative concentration inequalities on sample path space for mean field interaction. ESAIM-PROBAB STAT 2010. [DOI: 10.1051/ps:2008033] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
|