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Stochastic LQ Control with Extra Measurability Restriction: 《Journal of Systems Science & Complexity》2024年第3期1003-1022,共20页WANG Hongxia HU Yuxi LI Zixing SONG Lianfeng; supported by the Original Exploratory Program Project of National Natural Science Foundation of China under Grant No.62250056;the Joint Funds of the National Natural Science Foundation of China under Grant No.U23A20325;the Major Basic Research of Natural Science Foundation of Shandong Province under Grant No.ZR2021ZD14;the High-level Talent Team Project of Qingdao West Coast New Area under Grant No.RCTD-JC-2019-05。; Different from the standard linear quadratic(LQ)problem for stochastic systems,the LQ problem considered in the paper has extra measurability restrictions.The problem also appears in the LQ control problem for stochas...; 关键词：Multiplicative noise systems optimal control stochastic maximum principle stochastic systems

Representation of measures of noncompactness and its applications related to an initial value problem in Banach spaces被引量：1: 《Science China Mathematics》2023年第4期745-776,共32页Xiaoling Chen Lixin Cheng; supported by National Natural Science Foundation of China(Grant No.11731010)。; This paper is devoted to studying the representation of measures of non-generalized compactness,in particular,measures of noncompactness,of non-weak compactness and of non-super weak compactness,defined on Banach spac...; 关键词：representation of measures of noncompactness convex analysis Lebesgue-Bochner measurability integral inequality initial value problem in Banach spaces

Smoothness of invariant manifolds and foliations for in nite dimensional random dynamical systems--Dedicated to Professor Shantao Liao: 《Science China Mathematics》2020年第9期1877-1912,共36页Jun Shen Kening Lu Weinian Zhang; This work was supported by National Natural Science Foundation of China(Grant Nos.11501549,11331007,11971330,11771307,11831012 and 11726623);the Fundamental Research Funds for the Central Universities(Grant No.YJ201646).; In this paper,we investigate the smoothness of invariant manifolds and foliations for random dynamical systems with nonuniform pseudo-hyperbolicity in Hilbert spaces.We discuss on the effect of temperedness and the sp...; 关键词：random dynamical system invariant manifold invariant foliation pseudo-hyperbolicity MEASURABILITY

Formulation of Leggett–Garg Inequalities in Terms of q-Entropies: 《Communications in Theoretical Physics》2014年第9期320-326,共7页Alexey E. Rastegin; As is well known, the macroscopic realism and the noninvasive measurability together lead to Leggett–Garg inequalities violated by quantum mechanics. We consider tests of the Leggett–Garg type with use of the q-entr...; 关键词：BELL theorem Leggett–Garg INEQUALITIES macrorealism NONINVASIVE MEASURABILITY conditional q-entropies

Set-Valued Stochastic Integrals with Respect to Finite Variation Processes: 《Advances in Pure Mathematics》2013年第9期15-19,共5页Jinping Zhang Jiajia Qi; In a Euclidean space Rd, the Lebesgue-Stieltjes integral of set-valued stochastic processes with respect to real valued finite variation process is defined directly by employing all integrably bounded selections inste...; 关键词：SET-VALUED Stochastic PROCESS FINITE VARIATION PROCESS MEASURABILITY

Construction and Regularity of Transition Functions on Polish Spaces under Measurability Conditions被引量：1: 《Acta Mathematicae Applicatae Sinica》2013年第1期1-14,共14页Liu-er Ye Xian-ping Guo; Supported by the National Natural Science Foundation of China (No.10925107);Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme;the Fundamental Research Funds for the Central Universities (No.11612314); This paper concerns the construction and regularity of a transition （probability） function of a nonhomogeneous continuous-time Maxkov process with given transition rates and a general state space. Motivating from a ...; 关键词：Transition rate transition function construction and regularity measurability condition

Simultaneous Measurability of Error and Disturbance: 《Journal of Modern Physics》2013年第2期267-271,共5页Riuji Mochizuki; The uncertainty relation, which displays an elementary property of quantum theory, was originally described by Heisenberg as the relation between error and disturbance. Ozawa presented a more rigorous expression of th...; 关键词：Quantum LOGIC Uncertainty INEQUALITY

Several applications of the theory of random conjugate spaces to measurability problems被引量：4: 《Science China Mathematics》2007年第5期737-747,共11页Tie-xin GUO Department of Mathematics, School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083, China; the National Natural Science Foundation of China (Grant No. 10471115); The central purpose of this paper is to illustrate that combining the recently developed theory of random conjugate spaces and the deep theory of Banach spaces can, indeed, solve some difficult measurability problems ...; 关键词：random normed module random conjugate space measurability problem 46B09 46H25 46A22 46B22 60H25

THE STUDY ON A KIND OF CONTROL SYSTEM WITH NONLINEAR PARABOLIC DISTRIBUTED PARAMETERS: 《Applied Mathematics and Mechanics(English Edition)》2002年第2期178-186,共9页ZHOU Jian-jun(周建军) XU Yan-hou(徐燕侯); HESTUDtheNationalNaturalScienceFoundationofChina ( 5993 61 40 ); The modelling of one kind of nonlinear parabolic distributed parameter control system with moving boundary, which had extensive applications was presented, Two methods were used to investigate the basic characteristic...; 关键词：distributed parameter control system NONLINEAR moving boundary stability MEASURABILITY CONTROLLABILITY

Note on the Paper “Representation of Set Valued Operators” *: 《Journal of Mathematical Research and Exposition》1998年第3期326-328,共3页王晓敏薛小平; The aim of this paper is to show that one main theorem in is not correct by a counterexample and to give its correction.; 关键词：set valued operator support function measurability.

MEASURABILITY