We aim at accommodating the existing affine jump-diffusion and quadratic models under the same roof, namely the linear-quadratic jump-diffusion (LQJD) class. We give a complete characterization of the dynamics of this class by stating explicitly the structural constraints, as well as the admissibility conditions. This allows us to carry out a specification analysis for the 3-factor LQJD models. We compute the standard transform of the state vector relevant to asset pricing up to a system of ordinary differential equations. We show that the LQJD class can be embedded into the affine class through use of an augmented state vector. This establishes a one-to-one equivalence relationship between both classes in terms of transform analysis.

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Many scholars have conducted in-depth research on the theme of land use change and food security, and formed fruitful research results, but there is a lack of quantitative analysis and comprehensive evaluation of research achievements. Therefore, based on the relevant literature on the theme of land use change and food security in the core collection of the Web of Science (WOS) database, this paper takes the advantage of CiteSpace and VOSviewer bibliometric software to draw the cooperative network and keyword cooccurrence map to analyze the research progress and frontier. The results reveal that: (1) The research started in 1999 and can be divided into three stages: initial research, rapid development, and a stable in-depth stage. This topic has increasingly become a research hotspot in the academic community. (2) The distribution of research institutions is concentrated and forms a small cluster, and the research networks between developed and developing countries have been established, and developed countries are in the core position, but the cooperation network is not prominent. (3) The research content is becoming increasingly organized and systematic, and the research hot topics are divided into seven aspects. (4) The research area of the subject covers multiple levels, such as global, national, and specific natural geographical regions, and has formed a research system of geographic information technology and satellite remote sensing technology. It also presents the trend of cross integration with economics, land management and soil science. In the future, theoretical innovation still needs to be strengthened, and we should strengthen the research on the impact of agricultural chemical fertilizers on food security and study the impact of urban expansion on land use change.

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