VOL. 20 | 2023
 
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Articles
Anatoliy Malyarenko, Martin Ostoja-Starzewski
Probab. Surveys 20, 1-86, (2023) DOI: 10.1214/22-PS12 Open Access
KEYWORDS: Random field, Cosmic microwave background, microstructure, spectral expansion, 60G60, 74A40, 74E35, 74H50, 74S60, 76F55, 76M35
Julien Brémont
Probab. Surveys 20, 87-112, (2023) DOI: 10.1214/23-PS13 Open Access
KEYWORDS: Homogeneous random walk, oscillating random walk, recurrence criterion, 60G17, 60J10
Juraj Földes, David P. Herzog
Probab. Surveys 20, 113-169, (2023) DOI: 10.1214/22-PS11 Open Access
KEYWORDS: hypoelliptic operator, boundary-valued PDE, stochastic characteristics, 60H30, 35H10, 35G15, 60H10, 34B27, 35A01, 35A02
Peter J. Forrester
Probab. Surveys 20, 170-225, (2023) DOI: 10.1214/23-PS15 Open Access
KEYWORDS: Fluctuation formulas, linear statistics, random matrices, 60B20, 60F99
Madalina Deaconu, Antoine Lejay
Probab. Surveys 20, 226-290, (2023) DOI: 10.1214/23-PS14 Open Access
KEYWORDS: 60K35, 60K35, 60K35, SDE with jumps, Piecewise deterministic Markov process, Markov jump process, fragmentation equation
Michael Fleermann, Werner Kirsch
Probab. Surveys 20, 291-381, (2023) DOI: 10.1214/23-PS16 Open Access
KEYWORDS: Random matrix theory, method of moments, Stieltjes transform method, semicircle law, Marchenko-Pastur law, 60B20
Franziska Kühn, René L. Schilling
Probab. Surveys 20, 382-485, (2023) DOI: 10.1214/23-PS17 Open Access
KEYWORDS: maximal inequality, maximal function, moment estimate, tail estimate, concentration function, Burkholder–Davis–Gundy inequality, Doob’s maximal inequality, good-λ inequality, Hardy–Littlewood maximal function, martingale inequality, Gaussian process, Lévy process, Feller process, Lévy-type process, Markov process, Stochastic differential equation, 60E15, 60G15, 60G44, 60G51, 60G53, 60J25, 42B25, 42A61
Jared Chessari, Reiichiro Kawai, Yuji Shinozaki, Toshihiro Yamada
Probab. Surveys 20, 486-567, (2023) DOI: 10.1214/23-PS18 Open Access
KEYWORDS: BSDEs, Semilinear PDEs, Least-squares regression, Picard iteration, Malliavin calculus, Monte Carlo methods, deep learning, 65C30, 65C05, 93E24, 49L20, 60H07
Alexander Schnurr, Sebastian Rickelhoff
Probab. Surveys 20, 568-607, (2023) DOI: 10.1214/23-PS19 Open Access
KEYWORDS: Markov process, generator, killing, Lévy process, semimartingale characteristics, Stochastic differential equations, 60J76, 60H10, 60J25, 60G17
Alexander Nazarov, Yulia Petrova
Probab. Surveys 20, 608-663, (2023) DOI: 10.1214/23-PS20 Open Access
KEYWORDS: small ball probabilities, Gaussian processes, Hilbertian norm, Spectral asymptotics, 60-02, 60G15, 47G10, 34L05
Nikolay M. Babayan, Mamikon S. Ginovyan
Probab. Surveys 20, 664-721, (2023) DOI: 10.1214/23-PS21 Open Access
KEYWORDS: prediction error, deterministic and nondeterministic process, Spectral density, Ibragimov’s theorems, Rosenblatt’s theorems, Szegő’s condition, Transfinite diameter, eigenvalues of truncated Toeplitz matrices, 60G10, 60G25, 62M15, 62M20, 15A18‎, 30C10
Luis Fredes, Jean-François Marckert
Probab. Surveys 20, 722-801, (2023) DOI: 10.1214/23-PS22 Open Access
KEYWORDS: Random trees, Lattice trees, Spanning trees, Diffusion limited aggregation, Minimal spanning tree, random generation, 60C05, 60J10, 60F17, 60-02
Sylvain Dotti
Probab. Surveys 20, 802-836, (2023) DOI: 10.1214/23-PS23 Open Access
KEYWORDS: Cylindrical Wiener process, elementary processes, Itô integral, white noise theory, 60H05, 60J65, 60G99, 60H40
Ali Khezeli
Probab. Surveys 20, 837-896, (2023) DOI: 10.1214/20-PS340 Open Access
KEYWORDS: Gromov-Hausdorff metric, Gromov-Hausdorff-Prokhorov metric, boundedly-compact, functor, 60B05, 51F99
Dmitry Beliaev
Probab. Surveys 20, 897-937, (2023) DOI: 10.1214/23-PS24 Open Access
KEYWORDS: Smooth Gaussian fields, percolation, 60K35, 60D05, 60G15
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