Prof. Narn-Rueih Shieh 臺灣大學數學系

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演講演講者者：謝南瑞教授

Prof. Narn-Rueih Shieh 臺灣大學數學系

National Taiwan University

講講

題

題： Overviews on Stochastic Analysis

時時間間

：

2009 年 9 月 18 日 (星期五) 10:30-12:00

地地點：點臺灣大學數學系新數學館 405 室

摘摘要： In this talk, we review the development and the 要

essentials of stochastic analysis; with view toward the SA for exponential processes.

主主辦辦人人：謝南瑞教授 (臺灣大學數學系)

國家理論科學研究中心數學組(臺北辦公室) 臺大數學科學中心

NCTS/TPE & TIMS Joint Activity in Probability

相關事宜請與梁宜婷小姐聯絡 Tel:(02)3366-9927 歡迎上網查詢網址：http:// math.cts.ntu.edu.tw/

WXYZ 歡迎參加敬請公告 WXYZ

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演講演講者者：李兵博士

Dr. Bing Li

國家理論科學研究中心數學組(臺北辦公室) & 臺灣大學數學系

NCTS/TPE & National Taiwan University

講講

題

題： Probability in Symbolic Dynamics

時時間間

：

2009 年 9 月 25 日 (星期五) 10:30-12:00

地地點：點臺灣大學數學系新數學館 405 室

摘摘要要

： In this talk, we report some connections of probability theory and symbolic dynamical systems; with view toward the random continued fractions and the random covering problem.

主主辦辦人人：謝南瑞教授 (臺灣大學數學系)

國家理論科學研究中心數學組(臺北辦公室) 臺大數學科學中心

NCTS/TPE & TIMS Joint Activity in Probability

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演講演講者者：劉聚仁先生

Mr. Gi-Jen Liu

臺灣大學數學系

National Taiwan University

講講

題

題： Passive Tracer Transport in Stochastic Flows

時時間間

：

2009 年 10 月 2 日 (星期五) 10:30-12:00

地地點：點臺灣大學數學系新數學館 405 室

摘摘要要：In this talk, we report the passive transport problems

in random environments; with view toward W.A.

Woyczynski’s LNM 1800 Chapter 7

主主辦辦人人：謝南瑞教授 (臺灣大學數學系)

國家理論科學研究中心數學組(臺北辦公室) 臺大數學科學中心

NCTS/TPE & TIMS Joint Activity in Probability

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演演講講者：者劉聚仁先生 Mr. Gi-Jen Liu 臺灣大學數學系

National Taiwan University

講講題：題 Passive Tracer Transport in Stochastic Flows II

時時間間

：

2009 年 10 月 9 日 (星期五) 10:30-12:00

地地點：點臺灣大學數學系新數學館 405 室

摘摘要：In this talk, we report the passive transport problems 要

in random environments; with view toward W.A.

Woyczynski’s LNM 1800 Chapter 7

主主辦辦人：人謝南瑞教授 (臺灣大學數學系)

國家理論科學研究中心數學組(臺北辦公室) 臺大數學科學中心

NCTS/TPE & TIMS Joint Activity in Probability

相關事宜請與陳韻安小姐聯絡 Tel:(02)3366-3229 歡迎上網查詢網址：http:// math.cts.ntu.edu.tw/

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演演講者講者：孫嶸楓教授 Prof. Sun, Rongfeng

新加坡國立大學 National University of Singapore

講講題：題

Stochastic flows of kernels in the Brownian net and

the Brownian web

時時間： 2009 間

年 10 月 16 日 (星期五) 10:30-12:00

地地點：點

臺灣大學數學系新數學館 405 室

摘摘要要

：

Le Jan and Raimond developed a theory of stochastic flows of kernels, showing that each consistent family of n-point motions gives rise to a stochastic flow of kernel. As an

example, they constructed a special family of such flows where the underlying one-point motion is a Brownian motion on R. Recently, Howitt and Warren introduced a much more general class such flows on R, where the underlying n-point motions are Brownian motions with sticky interactions upon collision. Stochastic flows of kernels can be interpretated as random motion in a stationary space-time random environment, where the environment satisfies certain independent innovation properties. Here we give a graphical construction of the underlying environment for the Howitt-Warren flow in terms of the Brownian net (resp.

the Brownian web), which loosely speaking consists of a collection of branching-coalescing (resp. coalescing) Brownian motions starting from every point in the space-time plane. Almost sure path properties for the Howitt-Warren flow will also be derived. This is based on joint work in progress with Jan M. Swart (UTIA, Prague) and Emmanuel Schertzer (Columbia, New York).

主主辦辦人：謝南瑞教授 (臺灣大學數學系) 人

國家理論科學研究中心數學組(臺北辦公室) 臺大數學科學中心

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歡迎參加敬請公告

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Prof. Yi-Chiuan Chen Academia Sinica

Markov Shift and Anti-integrable limit in Dynamical Systems

2009 10 30 ( ) 10:30-12:00

405

An important way to understand the dynamics of maps is via the

symbolic dynamics. In this talk, I shall show examples the embedded Markov shift of which can be obtained in a very natural manner at their anti-integrable limits.

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演演講者講者：蕭守仁教授 Prof. Shoou-Ren Hsiau

國立彰化師範大學數學系

National Changhua University of Education

講講題題：

Optimal stopping problems in discrete time processes

時時間： 2009 間

年 11 月 6 日 (星期五) 10:30-12:00

地地點點：臺灣大學數學系新數學館 405 室

摘摘要：要

In this talk I will review several optimal stopping problems in discrete time processes and introduce some tools used in this area. The classical problems such as secretary problem , parking problem and their extensions will be addressed. The

theory of backward induction and the notion of monotone case will also be discussed.

主主辦辦人：謝南瑞教授 (臺灣大學數學系) 人

國家理論科學研究中心數學組(臺北辦公室) 臺大數學科學中心

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演演講者講者：陳冠宇教授 Prof. Guan-Yu Chen

國立交通大學應用數學系

National Chiao Tung University

講講題題：

On the mixing time for ergodic Markov chains

時時間間： 2009

年 11 月 13 日 (星期五) 10:30-12:00

地地點點：臺灣大學數學系新數學館 405 室

摘摘要：要

Markov chains with _nite states are used in a great variety of situations to ap-proximate, understand and sample from their limiting distributions. In the quanti-tative analysis of Markov chains, one is interested in the \mixing time" of the chain, that is, the time at which the chain gives a good approximation of its limiting dis-tribution. A remarkable phenomenon known as the cuto_ phenomenon reveals the observation that the distribution of the chain is a good approximation to the lim-iting distribution after the \cuto_ time"

but never _ts well before. This idea was introduced by D. Aldous and P. Diaconis in 1980s to capture the fact that some ergodic Markov chains converge abruptly to their invariant distributions. Such a phenomenon is closely related to the mixing time behavior which can be sensitive to measurement mechanics on the convergence of Markov chains to their stationar-ity. This is believed to happen frequently so that it makes sense to talk about the \mixing time". In this talk, we consider families of ergodic Markov processes, which include classical examples such as families of ergodic _nite Markov chains and Brownian motions on families of compact Riemannian manifolds. Under the measurement of Lp-norm, we will give criteria on the

examination of cuto_ phenomena. When p = 2, formulas on the L2-mixing time are available and will be illustrated with a couple of classical examples. 1

主主辦辦人：謝南瑞教授 (臺灣大學數學系) 人

國家理論科學研究中心數學組(臺北辦公室) 臺大數學科學中心

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演演講者講者：洪盟凱

教授 Prof. John M. Hong 中央大學數學系

National Central University

講講題：Sub-to-super transonic steady states and their linear 題

stabilities for gas flows.

時時間： 2009 間

年 11 月 27 日 (星期五) 10:30-12:00

地地點：臺灣大學數學系新數學館 405 室點

摘摘要：要

In this talk we consider the stability of sub-to-super transonic steady states of a one-dimensional model of isentropic compressible flows through a nozzle of

varying area with or without viscosity. These sub-to-super transonic steady states are newly found by using the geometric singular perturbation theory. We show that the sub-to-super steady states are physically relevant in the sense that they are linear stable as long as their velocities are great than 1/ sqr(2) of the sound speed.

主主辦辦人：謝南瑞教授 (臺灣大學數學系) 人

國家理論科學研究中心數學組(臺北辦公室) 臺大數學科學中心

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演講演講者者：曾文哲教授 Prof. Wen-Jer Tseng

淡江大學物理系 Tamkang University

講講題題：Genetic Switch in Periodically Changing Environments

時時間： 2009 間

年 12 月 25 日 (星期五) 10:30 -12:00

地地點點：臺灣大學數學系新數學館 405 室

摘摘要：要

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ecause all the cell populations are capable of making switches between different genetic expression states in response to the environmental change, it is natural to ask the question:

In a constantly fluctuating environment, which type of cell population (heterogeneous or homogeneous) is fitter in the long term? We take an extensive analysis about how the cell population evolves in a periodically switching environment either with symmetrical time-span or asymmetrical time-span. A complete picture of the phase diagrams for both cases is obtained.

Furthermore, we also explain in detail how the fitness problem bears much resemblance to the phenomenon, stochastic resonance, in physical sciences.

主主持持人：謝南瑞教授 (臺灣大學數學系) 人

國家理論科學研究中心數學組(臺北辦公室) 臺大數學科學中心

NCTS/TPE & TIMS Joint Activity in Probability

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歡迎參加敬請公告

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Prof. Narn-Rueih Shieh 臺灣大學數學系

演講 演 講者 者： 謝南瑞 教授