Noncommutative martingale deviation and Poincaré type inequalities with applications
We prove a deviation inequality for noncommutative martingales by extending Oliveira’s argument for random matrices. By integration we obtain a Burkholder type inequality with satisfactory constant. Using continuous time, we establish noncommutative Poincaré type inequalities for “nice” semigroups w...
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| Veröffentlicht in: | Probability theory and related fields 2015-04, Vol.161 (3-4), p.449-507 |
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| container_title | Probability theory and related fields |
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| creator | Junge, Marius Zeng, Qiang |
| description | We prove a deviation inequality for noncommutative martingales by extending Oliveira’s argument for random matrices. By integration we obtain a Burkholder type inequality with satisfactory constant. Using continuous time, we establish noncommutative Poincaré type inequalities for “nice” semigroups with a positive curvature condition. These results allow us to prove a general deviation inequality and a noncommutative transportation inequality due to Bobkov and Götze in the commutative case. To demonstrate our setting is general enough, we give various examples, including certain group von Neumann algebras, random matrices and classical diffusion processes, among others. |
| doi_str_mv | 10.1007/s00440-014-0552-1 |
| format | Article |
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| subjects | Algebra Brownian motion Constants Deviation Diffusion Economics Finance Group theory Inequalities Inequality Insurance Management Martingales Mathematical analysis Mathematical and Computational Biology Mathematical and Computational Physics Mathematics Mathematics and Statistics Operations Research/Decision Theory Probability Probability Theory and Stochastic Processes Quantitative Finance Statistics for Business Studies Theoretical Transportation |
| title | Noncommutative martingale deviation and Poincaré type inequalities with applications |
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