邵井海
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- 姓名:邵井海
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学科领域:
数理统计学
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邵井海,1978年11月生。1996年至2003年就读于北京师范大学数学系,获学士和硕士学位,后为北京师范大学与法国孛艮第大学联合培养博士生,并分别于2005年12月和2006年9月获得北京师范大学与孛艮第大学博士学位。现任教于北京师范大学。2007年获中国数学会钟家庆奖。主要研究兴趣:无穷维随机分析,泛函不等式。
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250
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成果数
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【期刊论文】transportation cost inequalities on path and loop groups
邵井海, shizan fang, jinghai shao
journal of functional analysis 218 (2005) 293–317,-0001,():
-1年11月30日
let g be a connected lie group with the lie algebra £: the action of cameron–martin space h(£) on the path space pe(g) introduced by l. gross (illinois j. math. 36 (1992) 447) is free. using this fact, we define the h-distance on pe(g); which enables us to establish a transportation cost inequality on pe(g): this method will be generalized to the path space over the loop group £e(g), so that we obtain a transportation cost inequality for heat measures on £e(g).
wasserstein distance, h-distance, loop groups, heat measures, girsanov theorem
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69浏览
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20分享
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【期刊论文】distance riemannienne, th
邵井海, shizan fang, jinghai shao,
c. r. acad. sci. paris, ser. i 341 (2005) 445–450,-0001,():
-1年11月30日
dans cette note, nous allons considérer la distance riemannienne sur le groupe des lacets, qui sera identifie à celle introduite par hino et ramirez[m. hino, j.a. ramirez, small-time gaussian behavior of symmetric diffusion semigroups, ann. probab. 31 (2003) 1254–1295]. une inégalité de transport est établie./ in this note, we shall consider the riemannian distance on loop groups, which will be identified to one introduced by hino and ramirez[m. hino, j.a. ramirez, small-time gaussian behavior of symmetric diffusion semigroups, ann. probab. 31 (2003) 1254–1295]. a transportation cost inequality is established.
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80浏览
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13分享
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263下载
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【期刊论文】hamilton–jacobi semi-groups in infinite dimensional spaces
邵井海, jinghai shao,
bull. sci. math. 130 (2006) 720–738,-0001,():
-1年11月30日
let (x, ρ) be a polish space endowed with a probability measure μ. assume that we can do malliavin calculus on (x,μ).let d :x × x→[0, ∞] be a pseudo-distance. consider qtf(x) = infy∈x{f(y) d2(x, y)/2t}. we shall prove that qtf satisfies the hamilton–jacobi inequality under suitable conditions. this result will be applied to establish transportation cost inequalities on path groups and loop groups in the spirit of bobkov, gentil and ledoux.
hamilton–jacobi semi-group, pseudo-distance, transportation cost inequalities, loop groups, malliavin calculus, heat measures
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34浏览
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12分享
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154下载
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【期刊论文】optimal transport maps for monge–kantorovich problem on loop groups
邵井海, shizan fang, jinghai shao
journal of functional analysis 248 (2007) 225–257,-0001,():
-1年11月30日
let g be a compact lie group, and consider the loop group leg := {ℓ∈ c([0, 1],g); ℓ (0) = ℓ (1) = e}.let ν be the heat kernel measure at the time 1. for any density function f on leg such that entν(f) <∞,we shall prove that there exists a unique optimal transportation map t: leg → leg which pushes ν forward to fν.
wasserstein distance, optimal transportation, monge–kantorovich problem, loop groups, riemannian distance, heat measures
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67浏览
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16分享
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