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[资源] 【转帖】如何学习概率

学习概率论的途径可以是多种多样的, 应当自己去体会摸索. 但如果你已经人在北大,而且有意在此方面发展的话,也许以下的建议可以供你参考.

课程学习;

【基础类】数学分析,高等代数,几何学,概率论,复变函数,实变函数,常微分方程,抽象代
数,

【专业类】应用随机过程,数理统计,测度论,泛函分析,偏微分方程,拓扑学,微分流形，
数学模型,集合论与图论

【其它学科】普通物理,理论力学,统计物理

【研究生】高等概率论,高等统计学,随机过程论,随机分析, 泛函分析II，随机过程选讲
I，近代偏微分方程，黎曼几何引论，概率极限定理，现代时间序列分析

　

建议学习顺序（北大本科-研究生连读）

第四学期：概率论

第五学期：应用随机过程，实变函数，数理统计

第六学期：测度论，泛函分析

第七学期：高等概率论，泛函分析II

第八学期：随机过程论，毕业论文讨论班

研究生第一学期：随机分析高等统计学，参加研究生讨论班

　

建议学习顺序（外校考入北大的研究生）

入学之前：自学测度论 (参考书：程士宏编著《测度论与概率论基础》，北京大学出版
社， 2003），

第一学期：高等概率论，应用随机过程泛函分析II 数理统计

第二学期：随机过程论，参加研究生讨论班

第三学期：随机分析，高等统计学

　

　

　

这里是美国数学会新近发布的有关概率论研究的综述报告

　

定期的学术会议和讨论班:

World Congress of the Bernoulli Society (每四年一次在世界各地举行)

Stochastic Processes and Their Applications (每年一次在世界各地举行)

The Saint Flour Summer School(每年夏天在法国举办)

全国概率统计学术会议(每四年一次在全国各地举行)

全国概率论年会(每四年一次在全国各地举行)

京津地区五四青年概率统计学术讨论会(每年五月在北京举行)

专业学会:

中国概率统计学会,

Institute of Mathematical Statistics (USA)

Bernoulli Society

专业杂志:

Annals of Probability (USA)

Probability Theory and Related Fields (Germany)

Communications in Mathematical Physics (USA)

Annals of Applied Probability (USA)

Stochastic Processes and Their Applications (World)

Annales de L'Institut Henri Poincare, Probabilites et Statistiques (France)

Journal of Applied Probablity (UK)

Advances on Applied Probability(UK)

　

电子期刊

Electronic Journal of Probability

Electronic Communications in Probability

Probability Abstract Service (PAS)

Probability Surveys, an open access electronic journal devoted to survey
papers in Probability, sponsored by the IMS and the Bernoulli Society.
Published papers and submission information can be viewed at the site
http://www.vtex.lt/ejournals/ps

and will shortly be viewable via Project Euclid
http://projecteuclid.org

Subscribers to PAS are encouraged to consider Probability Surveys
as a venue for publishing their next survey paper.

　

l
国际著名单位

Cornell University (Kesten, Lawler, Durrett, Saloff-Coste)

University of California, Berkeley (Aldous, Pitman, Peres, Evans)

University of British Columbia (Perkins, Barlow, Walsh，Slade)

http://www.math.ubc.ca/Research/probab.html

University of Paris VI (Le Gall，Marc Yor, Comet)
http://www.proba.jussieu.fr

ETH-Zentrum, Zurich

University of Cambridge

Bell Labs,

Technion,

Paris XI,

Stanford,

Madison,

Columbia

　

国际奖励

Loeve奖，由Berkekley统计系设立，奖励42岁以下的概率学家，到目前为止得主为
Aldous(Berkeley)

Telegrand, Le Gall， Peres, Schramm

　

Davidson奖, 由剑桥大学统计实验室设立，每年一人，我国候振挺教授，邹捷中教授曾
先后获此殊荣。

　

　

概率论和随机过程有热点问题吗？这是见仁见智的问题，可以参考的是近期概率杂志上
的题目，

以最近的Congress of the Bernoulli Society为例，在35个invited sessions，其中
13个为概率论。

10-Brownian motion

11-Coalescents, coagulation and fragmentation

12-Concentration inequalities

13-Conformal invariance and stochastic Loewner evolutions

14-Large deviations

15-Measure-valued processes and SPDE

16-Metastability

17-Mixing of finite Markov chains

18-Percolation, statistical mechanics, interacting particle systems

19-Probability on graphs

20-Random Matrices and Related Processes I

21-Random Matrices and Related Processes II

22-Random walks in random environments and random media
在2002北京召开的国家数学家大会上与概率论有关的邀请报告有

1-hour talks

H. Kesten Some highlights of percolation

N. Alon: Discrete Mathematics: Methods and Challenges (Section 4,
Probabilistic Method, also Goldwasser: The work of M. Sudan)

45-min talks

Section 10 Probability and Statistics

G Ben Arous: Aging and Spin-glass Dynamics

J. Bertoin: Some aspects of additive coalescents

E.Bolthausen: Localization-delocalization phenomena for random interfaces

M.F. Chen: Ergodic convergence rates of Markov processes

K.Johansson: Toeplitz determinant, random growth and determinantal processes

G.Lawler: Conformal invariance, universality and dimension of Brownian
frontier

Y. Peres: Brownian intersections, cover times and thick points via trees

A.Pisztora: Renormalizations, large deviations and phase separation in Ising
and percolation models

T.P. Speed: Biological Sequence Analysis

A.Y.Zaitsev: Estimates for the strong approximation in multi-dimensional
central limit theorem

O.Zeitouni: Random walks in random environments

Section 13 Mathematical Physics

J.-P. Eckmann: Non-Equilibrium Steady States

B.Nachtergaele & H-T Yau: Derivation of the Euler Equations from many-body
quantum mechanics

J.Bricmont: Ergodicity and mixing for stochastic partial differential
equations

Section 15 Mathematical Aspects of Computer Science

S.Arora: How NP got a New Definition: A survey of Probabilistically
checkable proofs

B.Impagliazzo: Hardness as randomness: a survey of universal derandomization

R. Kannan: Rapid mixing in Markov chains

Section 17 Application of Mathematics in the Sciences

Jia-an Yan: A numeraire-free and original probability based framework for
Financial markets

W.E: Energy landscapes and rare events

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