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Download Control Theory and Related Topics: In Memory of Prof Xunjing by Shanjian Tang, Jiongmin Yong PDF

By Shanjian Tang, Jiongmin Yong

Professor Xunjing Li (1935-2003) used to be a pioneer on top of things concept in China. He used to be influential within the chinese language group of utilized arithmetic, and the worldwide neighborhood of optimum keep watch over concept of dispensed parameter structures. He has made vitally important contributions to the optimum regulate conception of disbursed parameter platforms, specifically in regards to the first-order precious stipulations (Pontryagin-type greatest precept) for optimum regulate of nonlinear infinite-dimensional structures. This lawsuits quantity is a set of unique study papers or experiences authored or co-authored by means of Professor Li's former scholars, postdoctoral fellows, and mentored students within the components of regulate conception, dynamic structures, mathematical finance, and stochastic research, between others. those articles exhibit in some extent the effect of Professor Xunjing Li.

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Extra info for Control Theory and Related Topics: In Memory of Prof Xunjing Li, Fudan University, China, 3-5 June 2005

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S. for s ≤ t, A ∈ Fs , and Y ∈ L2 (Ft ). 3 means that an {Ft , 0 ≤ t ≤ T }-consistent expectation always has a BSDE representation if it is both E µ -dominated for some µ > 0 and constantpreserving. 4 for further details). Further, (H2)’ is stronger than (H2). 1. The above extended dynamic operator E can be shown to be identified to an {Ft , 0 ≤ t ≤ T }-consistent expectation E. 4. Let {Es,t [·], 0 ≤ s ≤ t ≤ T } be an {Ft , 0 ≤ t ≤ T }-consistent dynamic operator defined on L2+ (FT ) and satisfy (H1)’ and (H2)’.

35) The third axiom (E3) shows that an {Ft , 0 ≤ t ≤ T }-consistent expectation E[·] induces an {Ft , 0 ≤ t ≤ T }-consistent dynamic operator, which will be denoted by {Es,t [·], 0 ≤ s ≤ t ≤ T }. We shall identify them each other. Coquet et al. 3 proved the following representation result. 3. Assume that an {Ft , 0 ≤ t ≤ T }-consistent expectation {Es,t , 0 ≤ s ≤ t ≤ T } satisfies (H1)’ for some positive constant µ and the following assumption: (H2)’ Translation invariance. s. for s ≤ t, X ∈ L2 (Ft ) and Y ∈ L2 (Fs ).

B Both authors of this article were the beneficiaries of this new policy, though at different levels. 5in Chap10-Tribute 6 3. 1987—2001. Since 1985, a group of new researchers, mostly the new generation of graduate students after the class of 1977, started to join Professor Li’s research group. D’s from Europe and US returned to China and became the important new addition. Among others, most notable were the Post-doctor Shige Peng (France) and Associate Professor Jiongmin Yong (USA). In 1989, Professor Li, in collaboration with Jiongmin Yong, further extended the maximum principle to the general semilinear evolutionary distributed systems with mixed initial-terminal constraints, by using Ekeland’s Variational Principle and an improved “spike” variational method.

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