## Davis, Burgess

Compute Distance To:
 Author ID: davis.burgess Published as: Davis, Burgess; Davis, B. Homepage: http://www.stat.purdue.edu/~bdavis/ External Links: MGP
 Documents Indexed: 60 Publications since 1968 2 Contributions as Editor Co-Authors: 17 Co-Authors with 25 Joint Publications 495 Co-Co-Authors
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### Co-Authors

 34 single-authored 5 Bañuelos, Rodrigo 3 Lewis, John L. 3 Sitaramachandrarao, Rudrabhatla 2 Chen, Jeesen 2 Hosseini, Majid 2 Monroe, Itrel 2 Rubin, Herman 2 Volkov, Stanislav 1 Avis, David M. 1 Burkholder, Donald L. 1 Dean, Noah 1 McDonald, David R. 1 Perkins, Edwin A. 1 Peterson, Jonathon 1 Salisbury, Thomas S. 1 Song, Renming 1 Steele, J. Michael 1 Suh, Jiyeon 1 Zhang, Biao
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### Serials

 8 The Annals of Probability 5 Transactions of the American Mathematical Society 5 Probability Theory and Related Fields 4 Proceedings of the American Mathematical Society 3 Duke Mathematical Journal 3 Illinois Journal of Mathematics 3 Annals of Mathematical Statistics 2 Communications in Mathematical Physics 2 Indian Journal of Pure & Applied Mathematics 2 Journal of Functional Analysis 2 Journal of the London Mathematical Society. Second Series 2 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 2 Journal of Theoretical Probability 1 Israel Journal of Mathematics 1 Studia Mathematica 1 Arkiv för Matematik 1 Bulletin of the London Mathematical Society 1 Indiana University Mathematics Journal 1 Proceedings of the London Mathematical Society. Third Series 1 The New York Journal of Mathematics 1 Probability in the Engineering and Informational Sciences
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### Fields

 47 Probability theory and stochastic processes (60-XX) 8 Potential theory (31-XX) 6 Partial differential equations (35-XX) 5 Functions of a complex variable (30-XX) 5 Harmonic analysis on Euclidean spaces (42-XX) 3 Number theory (11-XX) 3 Operator theory (47-XX) 3 Statistics (62-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 History and biography (01-XX) 2 Global analysis, analysis on manifolds (58-XX) 1 Combinatorics (05-XX) 1 Measure and integration (28-XX) 1 Computer science (68-XX) 1 Operations research, mathematical programming (90-XX)

### Citations contained in zbMATH Open

42 Publications have been cited 578 times in 465 Documents Cited by Year
Reinforced random walk. Zbl 0665.60077
Davis, B.
1990
On the integrability of the martingale square function. Zbl 0211.21902
Davis, B.
1970
On the $$L^p$$ norms of stochastic integrals and other martingales. Zbl 0349.60061
Davis, Burgess
1976
On the weak type (1,1) inequality fo conjugate functions. Zbl 0259.42016
Davis, Burgess
1974
An elementary proof of the local central limit theorem. Zbl 0841.60013
Davis, Burgess; McDonald, David
1995
Continuous time vertex-reinforced jump processes. Zbl 1009.60027
Davis, Burgess; Volkov, Stanislav
2002
Intrinsic ultracontractivity and the Dirichlet Laplacian. Zbl 0766.47026
Davis, Burgess
1991
Brownian motion and random walk perturbed at extrema. Zbl 0930.60041
Davis, Burgess
1999
A geometrical characterization of intrinsic ultracontractivity for planar domains with boundaries given by the graphs of functions. Zbl 0836.60082
Bañuelos, Rodrigo; Davis, Burgess
1992
Vertex-reinforced jump processes on trees and finite graphs. Zbl 1048.60062
Davis, Burgess; Volkov, Stanislav
2004
Heat kernel, eigenfunctions, and conditioned Brownian motion in planar domains. Zbl 0676.60073
Bañuelos, Rodrigo; Davis, Burgess
1989
Brownian motion and analytic functions. Zbl 0421.60072
Davis, Burgess
1979
Some identities involving the Riemann zeta-function. II. Zbl 0614.10013
Sitaramachandrarao, R.; Davis, B.
1986
Picard’s theorem and Brownian motion. Zbl 0292.60126
Davis, Burgess
1975
Hardy spaces and rearrangements. Zbl 0438.42010
Davis, Burgess
1980
Weak limits of perturbed random walks and the equation $$Y_ t = B_ t+\alpha\sup\{Y_ s:s \leq t\} + \beta\inf\{Y_ s:s\leq t\}$$. Zbl 0870.60076
Davis, Burgess
1996
Conditioned Brownian motion in planar domains. Zbl 0663.60060
Davis, Burgess
1988
On the spectral gap for fixed membranes. Zbl 1021.35040
Davis, Burgess
2001
On the distributions of conjugate functions of nonnegative measures. Zbl 0271.60090
Davis, Burgess
1973
Stopping rules for $$S_ n/n$$, and the class $$L \log L$$. Zbl 0194.50102
Davis, B.
1971
Sharp estimates for Dirichlet eigenfunctions in horn-shaped regions. Zbl 0772.35042
Bañuelos, Rodrigo; Davis, Burgess
1992
Reinforced and perturbed random walks. Zbl 0953.60028
Davis, Burgess
1999
On Brownian slow points. Zbl 0506.60078
Davis, Burgess
1983
Brownian slow points: The critical case. Zbl 0576.60030
Davis, Burgess; Perkins, Edwin
1985
Moments of the lifetime of conditioned Brownian motion in cones. Zbl 0805.60079
Davis, Burgess; Zhang, Biao
1994
On the integrability of the ergodic maximal function. Zbl 0496.28017
Davis, Burgess
1982
Paths for subharmonic functions. Zbl 0541.31001
Davis, Burgess; Lewis, John L.
1984
Probabilistic analysis of a greedy heuristic for Euclidean matching. Zbl 1134.90468
Avis, David; Davis, Burgess; Steele, J. Michael
1988
Loss of recurrence in reinforced random walk. Zbl 0685.60073
Davis, Burgess
1989
Recurrence and transience preservation for vertex reinforced jump processes in one dimension. Zbl 1266.60163
Davis, Burgess; Dean, Noah
2010
On Kolmogorov’s inequalities $$\|\tilde f\|_p\leq C_p\| f\|_1$$, $$0<p<1$$. Zbl 0306.31009
Davis, Burgess
1976
On the Barlow-Yor inequalities for local time. Zbl 0617.60041
Davis, Burgess
1987
Excited random walks with non-nearest neighbor steps. Zbl 1408.60035
Davis, Burgess; Peterson, Jonathon
2017
Connecting Brownian paths. Zbl 0658.60111
Davis, Burgess; Salisbury, Thomas S.
1988
Erratum: Sharp estimates for Dirichlet eigenfunctions in Horn-shaped regions. Zbl 0805.35082
Bañuelos, Rodrigo; Davis, Burgess
1994
On ratio inequalities for heat content. Zbl 1122.35037
Davis, Burgess; Hosseini, Majid
2004
Moments of random walk having infinite variance and the e istence of certain optimal stopping rules for $$S_n/n$$. Zbl 0249.60013
Davis, Burgess
1973
Selected works of Donald L. Burkholder. Edited by Burgess Davis and Renming Song. Zbl 1271.01046
Burkholder, Donald L.
2011
Divergence properties of some martingale transforms. Zbl 0185.45101
Davis, B.
1969
On Burkholder’s supermartingales. Zbl 1098.60042
Davis, Burgess; Suh, Jiyeon
2006
On time changing continuous martingales to Brownian motion. Zbl 1268.60054
Davis, Burgess
2004
An extremal property of some capacitary measures in E$$_n$$. Zbl 0243.31008
Davis, Burgess; Lewis, John L.
1973
Excited random walks with non-nearest neighbor steps. Zbl 1408.60035
Davis, Burgess; Peterson, Jonathon
2017
Selected works of Donald L. Burkholder. Edited by Burgess Davis and Renming Song. Zbl 1271.01046
Burkholder, Donald L.
2011
Recurrence and transience preservation for vertex reinforced jump processes in one dimension. Zbl 1266.60163
Davis, Burgess; Dean, Noah
2010
On Burkholder’s supermartingales. Zbl 1098.60042
Davis, Burgess; Suh, Jiyeon
2006
Vertex-reinforced jump processes on trees and finite graphs. Zbl 1048.60062
Davis, Burgess; Volkov, Stanislav
2004
On ratio inequalities for heat content. Zbl 1122.35037
Davis, Burgess; Hosseini, Majid
2004
On time changing continuous martingales to Brownian motion. Zbl 1268.60054
Davis, Burgess
2004
Continuous time vertex-reinforced jump processes. Zbl 1009.60027
Davis, Burgess; Volkov, Stanislav
2002
On the spectral gap for fixed membranes. Zbl 1021.35040
Davis, Burgess
2001
Brownian motion and random walk perturbed at extrema. Zbl 0930.60041
Davis, Burgess
1999
Reinforced and perturbed random walks. Zbl 0953.60028
Davis, Burgess
1999
Weak limits of perturbed random walks and the equation $$Y_ t = B_ t+\alpha\sup\{Y_ s:s \leq t\} + \beta\inf\{Y_ s:s\leq t\}$$. Zbl 0870.60076
Davis, Burgess
1996
An elementary proof of the local central limit theorem. Zbl 0841.60013
Davis, Burgess; McDonald, David
1995
Moments of the lifetime of conditioned Brownian motion in cones. Zbl 0805.60079
Davis, Burgess; Zhang, Biao
1994
Erratum: Sharp estimates for Dirichlet eigenfunctions in Horn-shaped regions. Zbl 0805.35082
Bañuelos, Rodrigo; Davis, Burgess
1994
A geometrical characterization of intrinsic ultracontractivity for planar domains with boundaries given by the graphs of functions. Zbl 0836.60082
Bañuelos, Rodrigo; Davis, Burgess
1992
Sharp estimates for Dirichlet eigenfunctions in horn-shaped regions. Zbl 0772.35042
Bañuelos, Rodrigo; Davis, Burgess
1992
Intrinsic ultracontractivity and the Dirichlet Laplacian. Zbl 0766.47026
Davis, Burgess
1991
Reinforced random walk. Zbl 0665.60077
Davis, B.
1990
Heat kernel, eigenfunctions, and conditioned Brownian motion in planar domains. Zbl 0676.60073
Bañuelos, Rodrigo; Davis, Burgess
1989
Loss of recurrence in reinforced random walk. Zbl 0685.60073
Davis, Burgess
1989
Conditioned Brownian motion in planar domains. Zbl 0663.60060
Davis, Burgess
1988
Probabilistic analysis of a greedy heuristic for Euclidean matching. Zbl 1134.90468
Avis, David; Davis, Burgess; Steele, J. Michael
1988
Connecting Brownian paths. Zbl 0658.60111
Davis, Burgess; Salisbury, Thomas S.
1988
On the Barlow-Yor inequalities for local time. Zbl 0617.60041
Davis, Burgess
1987
Some identities involving the Riemann zeta-function. II. Zbl 0614.10013
Sitaramachandrarao, R.; Davis, B.
1986
Brownian slow points: The critical case. Zbl 0576.60030
Davis, Burgess; Perkins, Edwin
1985
Paths for subharmonic functions. Zbl 0541.31001
Davis, Burgess; Lewis, John L.
1984
On Brownian slow points. Zbl 0506.60078
Davis, Burgess
1983
On the integrability of the ergodic maximal function. Zbl 0496.28017
Davis, Burgess
1982
Hardy spaces and rearrangements. Zbl 0438.42010
Davis, Burgess
1980
Brownian motion and analytic functions. Zbl 0421.60072
Davis, Burgess
1979
On the $$L^p$$ norms of stochastic integrals and other martingales. Zbl 0349.60061
Davis, Burgess
1976
On Kolmogorov’s inequalities $$\|\tilde f\|_p\leq C_p\| f\|_1$$, $$0<p<1$$. Zbl 0306.31009
Davis, Burgess
1976
Picard’s theorem and Brownian motion. Zbl 0292.60126
Davis, Burgess
1975
On the weak type (1,1) inequality fo conjugate functions. Zbl 0259.42016
Davis, Burgess
1974
On the distributions of conjugate functions of nonnegative measures. Zbl 0271.60090
Davis, Burgess
1973
Moments of random walk having infinite variance and the e istence of certain optimal stopping rules for $$S_n/n$$. Zbl 0249.60013
Davis, Burgess
1973
An extremal property of some capacitary measures in E$$_n$$. Zbl 0243.31008
Davis, Burgess; Lewis, John L.
1973
Stopping rules for $$S_ n/n$$, and the class $$L \log L$$. Zbl 0194.50102
Davis, B.
1971
On the integrability of the martingale square function. Zbl 0211.21902
Davis, B.
1970
Divergence properties of some martingale transforms. Zbl 0185.45101
Davis, B.
1969
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### Cited by 542 Authors

 21 Osękowski, Adam 16 Bañuelos, Rodrigo 10 Burdzy, Krzysztof 10 Khoshnevisan, Davar 9 Collevecchio, Andrea 9 Davis, Burgess 9 Tarrès, Pierre 9 Volkov, Stanislav 7 Kulczycki, Tadeusz 6 Kious, Daniel 6 Merkl, Franz 6 Rolles, Silke W. W. 6 Sabot, Christophe 6 Smits, Robert G. 6 Weisz, Ferenc 6 Zhang, Tusheng S. 5 Conus, Daniel 5 Deblassie, Dante 5 Kozma, Gady 5 Mohan, Manil Thankamani 5 Pemantle, Robin 5 Schapira, Bruno 5 Shcherbakov, Vadim 5 Singh, Arvind 4 Basdevant, Anne-Laure 4 Großkinsky, Stefan 4 Holmes, Mark P. 4 Joseph, Mathew 4 Mountford, Thomas S. 4 Murata, Minoru 4 Øksendal, Bernt Karsten 4 Randrianantoanina, Narcisse 4 Sidoravicius, Vladas 4 Sleeman, Brian David 4 Takei, Masato 4 Yor, Marc 3 Aikawa, Hiroaki 3 Bass, Richard F. 3 Chleboun, Paul 3 Disertori, Margherita 3 Fontelos López, Marco Antonio 3 Janakiraman, Prabhu 3 Jiao, Yong 3 Kaleta, Kamil 3 Kubo, Akisato 3 Li, Baoqin 3 Li, Deli 3 Limic, Vlada 3 Liu, Wei 3 Markowsky, Greg T. 3 Pamuk, Serdal 3 Parcet, Javier 3 Raimond, Olivier 3 Röckner, Michael 3 Shiu, Shang-Yuan 3 Song, Renming 3 Vela-Pérez, María 3 Wu, Lian 3 Yabuta, Kôzô 3 Zeng, Xiaolin 2 Amir, Gideon 2 Athreya, Krishna Balasundaram 2 Barlow, Martin T. 2 Bauerschmidt, Roland 2 Benaïm, Michel 2 Benjamini, Itai 2 Blouhi, Tayeb 2 Bogus, Kamil 2 Boudabra, Maher 2 Burkholder, Donald L. 2 Capasso, Vincenzo 2 Chen, Yong 2 Chen, Zhen-Qing 2 Coja-Oghlan, Amin 2 Collet, Pierre 2 Cotar, Codina 2 Cranston, Michael Craig 2 Crawford, Nicholas 2 Dai Pra, Paolo 2 Dai, Jack Jie 2 Dolgopyat, Dmitry 2 Ephremidze, Lasha 2 Friedman, Avner 2 Gao, Hongjun 2 Goldsheid, Ilya Ya. 2 Griffin, Philip S. 2 Gut, Allan 2 Hausenblas, Erika 2 Helmuth, Tyler 2 Herz, Carl S. 2 Hiderah, Kamal 2 Hong, Guixiang 2 Hosseini, Majid 2 Hou, Xianming 2 Janson, Svante 2 Junge, Marius 2 Kabluchko, Zakhar A. 2 Kim, Panki 2 Kosygina, Elena 2 Kovač, Vjekoslav ...and 442 more Authors
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### Cited in 145 Serials

 30 Probability Theory and Related Fields 29 Journal of Functional Analysis 23 The Annals of Probability 21 Transactions of the American Mathematical Society 21 Statistics & Probability Letters 20 Stochastic Processes and their Applications 14 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 13 Proceedings of the American Mathematical Society 12 Potential Analysis 11 Journal of Statistical Physics 10 Journal of Mathematical Analysis and Applications 9 Stochastic Analysis and Applications 9 The Annals of Applied Probability 9 Electronic Journal of Probability 7 Communications in Mathematical Physics 7 Journal of Theoretical Probability 6 Illinois Journal of Mathematics 6 Bernoulli 5 Mathematische Zeitschrift 5 Acta Mathematica Hungarica 4 Advances in Applied Probability 4 Analysis Mathematica 4 Mathematical Biosciences 4 Arkiv för Matematik 4 Annales de l’Institut Fourier 4 Revista Matemática Iberoamericana 4 Combinatorics, Probability and Computing 4 Electronic Communications in Probability 4 ALEA. Latin American Journal of Probability and Mathematical Statistics 3 Mathematical Notes 3 Mathematical Proceedings of the Cambridge Philosophical Society 3 Duke Mathematical Journal 3 Journal of Differential Equations 3 Tohoku Mathematical Journal. Second Series 3 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 3 The Journal of Geometric Analysis 3 Communications in Partial Differential Equations 3 Bulletin of the American Mathematical Society. New Series 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Frontiers of Mathematics in China 2 The Canadian Journal of Statistics 2 Israel Journal of Mathematics 2 Journal of Mathematical Biology 2 Mathematical Methods in the Applied Sciences 2 Advances in Mathematics 2 Archiv der Mathematik 2 Bulletin de la Société Mathématique de France 2 Inventiones Mathematicae 2 Journal of the Mathematical Society of Japan 2 Journal of Soviet Mathematics 2 Applied Mathematics Letters 2 Journal of the American Mathematical Society 2 Queueing Systems 2 SIAM Journal on Mathematical Analysis 2 Monte Carlo Methods and Applications 2 Journal of Theoretical Biology 2 Stochastic and Partial Differential Equations. Analysis and Computations 1 Applicable Analysis 1 Journal d’Analyse Mathématique 1 Journal of Mathematical Physics 1 Physica A 1 Rocky Mountain Journal of Mathematics 1 Studia Mathematica 1 Mathematics of Computation 1 Bulletin of Mathematical Biology 1 Theory of Probability and its Applications 1 Acta Mathematica 1 The Annals of Statistics 1 Bulletin of the London Mathematical Society 1 Collectanea Mathematica 1 Compositio Mathematica 1 Czechoslovak Mathematical Journal 1 Integral Equations and Operator Theory 1 Journal of Approximation Theory 1 Journal of Combinatorial Theory. Series B 1 Journal of Computational and Applied Mathematics 1 Journal of the London Mathematical Society. Second Series 1 Journal of Mathematical Psychology 1 Journal of Multivariate Analysis 1 Journal of Statistical Planning and Inference 1 Manuscripta Mathematica 1 Mathematische Nachrichten 1 Memoirs of the American Mathematical Society 1 Michigan Mathematical Journal 1 Monatshefte für Mathematik 1 Nagoya Mathematical Journal 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 SIAM Journal on Numerical Analysis 1 Siberian Mathematical Journal 1 Mathematical Social Sciences 1 Probability and Mathematical Statistics 1 Acta Applicandae Mathematicae 1 Optimization 1 Constructive Approximation 1 Algorithmica 1 Mathematical and Computer Modelling 1 Asymptotic Analysis 1 Journal of Scientific Computing 1 Sugaku Expositions ...and 45 more Serials
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### Cited in 38 Fields

 341 Probability theory and stochastic processes (60-XX) 70 Partial differential equations (35-XX) 61 Harmonic analysis on Euclidean spaces (42-XX) 35 Statistical mechanics, structure of matter (82-XX) 31 Functional analysis (46-XX) 30 Potential theory (31-XX) 23 Functions of a complex variable (30-XX) 22 Biology and other natural sciences (92-XX) 19 Operator theory (47-XX) 18 Combinatorics (05-XX) 14 Global analysis, analysis on manifolds (58-XX) 13 Quantum theory (81-XX) 12 Statistics (62-XX) 10 Real functions (26-XX) 10 Several complex variables and analytic spaces (32-XX) 10 Numerical analysis (65-XX) 8 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 7 Fluid mechanics (76-XX) 6 Measure and integration (28-XX) 5 Dynamical systems and ergodic theory (37-XX) 5 Integral transforms, operational calculus (44-XX) 5 Operations research, mathematical programming (90-XX) 4 Ordinary differential equations (34-XX) 4 Approximations and expansions (41-XX) 2 Special functions (33-XX) 2 Abstract harmonic analysis (43-XX) 2 Computer science (68-XX) 2 Mechanics of deformable solids (74-XX) 1 History and biography (01-XX) 1 Number theory (11-XX) 1 Field theory and polynomials (12-XX) 1 Topological groups, Lie groups (22-XX) 1 Difference and functional equations (39-XX) 1 Sequences, series, summability (40-XX) 1 Integral equations (45-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Differential geometry (53-XX) 1 Systems theory; control (93-XX)