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L^(p)Solution of Reflected BSDEs with One Continuous Barrier and Quasi-linear Growth Generators

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Acta Mathematicae Applicatae Sinica 2024年第4期40卷 943-953页

作者： Sheng-jun fan School of Mathematics China University of Mining and TechnologyXuzhou 221116China

This paper is devoted to solving a reflected backward stochastic differential equation(BSDE in short)with one continuous barrier and a quasi-linear growth generator g,which has a linear growth in(y,z),except the upper direction in case of y1)solutions for the reflected *** also prove that the minimal Lpsolution can be approximated by a sequence of Lpsolutions of certain reflected BSDEs with Lipschitz generators.

关键词： Reflected BSDEs Quasi-linear growth L^(p)solution Existence Comparison theorem

Properties of Solutions of BSDEs with Integrable Parameters

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Acta Mathematicae Applicatae Sinica 2007年第4期23卷 697-704页

作者： Sheng-jun fan College of Sciences China University of Mining & Technology Xuzhou 221008 China

The main result of this study is to obtain, using the localization method in Briand et al. Levi, Fatou and Lebesgue type theorems for the solutions of certain one-dimensional backward stochastic differential equation ... 详细信息

关键词： Backward stochastic differential equation integrable parameters Lebesgue theorem

Correlation between movement of tectonic blocks and earthquakes in groups

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Acta Seismologica Sinica(English Edition) 2001年第5期14卷 547-555页

作者： fan jun-xi 1. Institute of Geology China Seismological Bureau 100029 Beijing China 2. Tectonophysics Laboratory China Seismological Bureau 100029 Beijing China 3. Seismological Bureau of Hebei Province 050021 Shijiazhuang China

The Chinese mainland is divided into some tectonic blocks by nearly NE- and EW-orientated faults. Meanwhile strong earthquakes in the Chinese mainland usually cluster in time and space. We call 'earthquakes in groups'. Tectonic blocks separated by faults and earthquakes in groups are prominent features of the tectonics of the Chinese mainland. Correlation between movement of tectonic blocks and groups of earthquakes is discussed in this paper. The results show that earthquakes in groups often occurred at one or several block boundary faults. The released elastic strain energy is built up in the same periods and around blocks. It means that strong earthquakes in groups are mainly caused by movement of blocks. Four types of block movement are identified based on group earthquakes: movement along a single boundary of a block (or a combined blocks), movement of a single block, movement of multi-blocks, and movement in block interiors. If we consider distribution of all strong earthquakes occurred in the Chinese mainland, the movement along a single boundary of a block is more popular one inducing strong earthquakes. But if we only consider earthquakes in groups rather than single earthquakes the movement of a block dominates among four modes. Statistics with respect to group earthquakes show that the Taihangshan mountain and the North China block are much active in the eastern part of Chinese mainland, and in western part of Chinese mainland the active blocks are Sichuan-Yunnan and the Kunlun-Songpan ones.

关键词： tectonic block earthquakes in groups types of block movement

Existence, Uniqueness and Approximation for Lp Solutions of Reflected BSDEs with Generators of One-sided Osgood Type

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Acta Mathematica Sinica,English Series 2017年第6期33卷 807-838页

作者： Sheng jun fan School of Mathematics China University of Mining and Technology Xuzhou 221116 P. R. China

We prove several existence and uniqueness results for Lp （p 〉 1） solutions of reflected BSDEs with continuous barriers and generators satisfying a one-sided Osgood condition together with a general growth condition in y and a uniform continuity condition or a linear growth condition in z. A necessary and sufficient condition with respect to the growth of barrier is also explored to ensure the existence of a solution. And, we show that the solutions may be approximated by the penalization method and by some sequences of solutions of reflected BSDEs. These results are obtained due to the development of those existing ideas and methods together with the application of new ideas and techniques, and they unify and improve some known works.

关键词： Reflected backward stochastic differential equation Lp solutions comparison theorem,one-sided Osgood condition uniform continuity condition

A Note on Jensen’s Inequality for BSDEs

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Acta Mathematica Sinica,English Series 2009年第10期25卷 1681-1692页

作者： Sheng jun fan College of Sciences China University of Mining ~z Technology Xuzhou 221008 P. R. China

Under the Lipschitz assumption and square integrable assumption on g, Jiang proved that Jensen＇s inequality for BSDEs with generator g holds in general if and only if g is independent of y, g is super homogenous in z and g（t, 0） = 0, a.s., a.e.. In this paper, based on Jiang＇s results, under the same assumptions as Jiang＇s, we investigate the necessary and sufficient condition on g under which Jensen＇s inequality for BSDEs with generator g holds for some specific convex functions, which generalizes some known results on Jensen＇s inequality for BSDEs.

关键词： backward stochastic differential equation Jensen's inequality g-expectation Jensen's inequality for BSDEs

Moment Inequality and Hlder Inequality for BSDEs

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Acta Mathematicae Applicatae Sinica 2009年第1期25卷 11-20页

作者： Sheng-jun fan College of School China University of Mining and Technology Xuzhou 221008 China

Under the Lipschitz and square integrable assumptions on the generator g of BSDEs, this paper proves that if g is positively homogeneous in （y, z） and is decreasing in y, then the Moment inequality for BSDEs with generator g holds in general, and if g is positively homogeneous and sub-additive in （y, z）, then the HSlder inequality and Minkowski inequality for BSDEs with generator g hold in general.

关键词： Backward stochastic differential equation moment inequality for bsdes hSlder inequality forbsdes minkowski inequality for BSDEs

A Relationship Between the Conditional g-Evaluation System and the Generator g and Its Applications

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Acta Mathematica Sinica,English Series 2007年第8期23卷 1427-1434页

作者： Sheng jun fan College of Sciences China University of Mining and Technology Xuzhou 221008 P. R. China

In this paper, under the most elementary conditions on a backward stochastic differential equation （BSDE for short） introduced by Peng, a new relationship between the conditional g-evaluation system and the generator g of BSDE is obtained in the sense of ＂process＂, based on some recent results of Jiang. Moreover, as applications, two converse comparison theorems and two uniqueness theorems on the generators of BSDEs are proved.

关键词： backward stochastic differential equation g-evaluation g-expectation generator converse comparison theorem

Picard Values and the Growth of Meromorphic Functions

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Acta Mathematica Sinica,English Series 2013年第10期29卷 1981-1992页

作者： jun fan CHEN Department of Mathematics Fujian Normal University

The purpose of this paper is to investigate the growth of meromorphic functions concern- ing Picard values with a radially distributed value. This generalizes a classic result due to Hayman [Hayman, W. K.： Picard val... 详细信息

关键词： Meromorphic function growth radial distribution deficiency angular domain

Real-time prediction of the motion tendency of human lower limbs during gait

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The Journal of China Universities of Posts and Telecommunications 2020年第4期27卷 1-7页

作者： Chen Faquan fan jun School of Mechanical Engineering Xinjiang UniversityUrumqi 830046China

Aiming at the problem of hysteresis in the human motion intention recognition algorithm based on kinematic sensors, a real-time prediction method about human lower limb motion tendency is proposed. It could be used to control exoskeleton robots, intelligent prosthes and other equipments in advance to eliminate the hysteresis of equipment movement. Firstly, the angle signals of ankle, knee and hip are segmented by the extreme points. Secondly, the multi-dimensional temporal association rules algorithm is used to analyze the angle signals to find out the relationships between signal patterns in adjacent time segments. Finally, the signal patterns at the next moment are predicted through the association rules algorithm, so as to predict the motion tendency of human lower limbs. Experimental results show that the proposed scheme achieves an average prediction accuracy of 78.3% for each signal segment, and can predict the subsequent motion of human lower limbs in average 92.24 ms.

关键词： motion prediction multi-dimensional temporal association rules signal processing