We show that a weak sense stationary stochastic process can be approximated by local averages. Explicit error bounds are given. Our result improves an early one from Splettst?sser.
The paper is concerned with optimal control of backward stochastic differentiM equation （BSDE） driven by Teugel＇s martingales and an independent multi-dimensional Brownian motion, where Teugel＇s martingales are a ...The paper is concerned with optimal control of backward stochastic differentiM equation （BSDE） driven by Teugel＇s martingales and an independent multi-dimensional Brownian motion, where Teugel＇s martingales are a family of pairwise strongly orthonormal martingales associated with L6vy processes （see e.g., Nualart and Schoutens＇ paper in 2000）. We derive the necessary and sufficient conditions for the existence of the optimal control by means of convex variation methods and duality techniques. As an application, the optimal control problem of linear backward stochastic differential equation with a quadratic cost criteria （or backward linear-quadratic problem, or BLQ problem for short） is discussed and characterized by a stochastic Hamilton system.展开更多
Despite recent interest in microbial diversity and community structure of lakes across various spatial scales, a global biogeographic distribution pattern and its controlling factors have not been fully disclosed. Her...Despite recent interest in microbial diversity and community structure of lakes across various spatial scales, a global biogeographic distribution pattern and its controlling factors have not been fully disclosed. Here, we compiled and analyzed 88,334,735 environmental 16S rRNA sequences from 431 lakes across a wide range of geographical distance and environmental conditions(in particular, salinity, 0–373.3 gL^–1). Our results showed that lake sediments inhabit significantly(ANOVA: P<0.001) more diverse microbial communities than lake waters. Non-metric dimensional scaling(NMDS) ordinations indicated that microbial community compositions differed distinctly among sample types(freshwater vs. saline, water vs. sediment) and geographic locations. Mantel and partial Mantel tests showed that microbial community composition in lake water was significantly(P=0.001) correlated with geographic distance, salinity, and pH. Statistical analyses based on neutral community and null models indicated that stochastic processes may play predominant roles in shaping the microbial biogeographic distribution patterns in the studied global lake waters. The dispersal-related stochasticity(e.g., homogenizing dispersal) exhibited a stronger influence on the distribution of microbial community in freshwater lakes than in saline lakes. Overall, this work expands our understanding of the impact of geographic distance, environmental conditions, and stochastic processes on microbial distribution in global lakes.展开更多
基金This work was supported partially by the National Natural Science Foundation of China (Grant Nos. 60472042,10571089 and 60572113),the Liuhui Center for Applied Mathematics, the Program for New Century Excellent Talents in Universitiesthe Research Fund for the Doctoral Program of Higher Educationthe Scientific Research Foundation for the Returned Overseas Chinese Scholars, Ministry of Education of China
文摘We show that a weak sense stationary stochastic process can be approximated by local averages. Explicit error bounds are given. Our result improves an early one from Splettst?sser.
基金supported by National Natural Science Foundation of China (Grant No. 11101090, 11101140, 10771122)Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20090071120002)+2 种基金Innovation Team Foundation of the Department of Education of Zhejiang Province (Grant No. T200924)Natural Science Foundation of Zhejiang Province (Grant No. Y6110775, Y6110789)Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry
文摘The paper is concerned with optimal control of backward stochastic differentiM equation （BSDE） driven by Teugel＇s martingales and an independent multi-dimensional Brownian motion, where Teugel＇s martingales are a family of pairwise strongly orthonormal martingales associated with L6vy processes （see e.g., Nualart and Schoutens＇ paper in 2000）. We derive the necessary and sufficient conditions for the existence of the optimal control by means of convex variation methods and duality techniques. As an application, the optimal control problem of linear backward stochastic differential equation with a quadratic cost criteria （or backward linear-quadratic problem, or BLQ problem for short） is discussed and characterized by a stochastic Hamilton system.
基金supported by grants from the National Natural Science Foundation of China (91751206, 41521001, 41602346, 41572328, 41630103)the 111 Program (State Administration of Foreign Experts Affairs & the Ministry of Education of China, grant B18049)+1 种基金Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan)State Key Laboratory of Biogeology and Environmental Geology, CUG (GBL11805)
文摘Despite recent interest in microbial diversity and community structure of lakes across various spatial scales, a global biogeographic distribution pattern and its controlling factors have not been fully disclosed. Here, we compiled and analyzed 88,334,735 environmental 16S rRNA sequences from 431 lakes across a wide range of geographical distance and environmental conditions(in particular, salinity, 0–373.3 gL^–1). Our results showed that lake sediments inhabit significantly(ANOVA: P<0.001) more diverse microbial communities than lake waters. Non-metric dimensional scaling(NMDS) ordinations indicated that microbial community compositions differed distinctly among sample types(freshwater vs. saline, water vs. sediment) and geographic locations. Mantel and partial Mantel tests showed that microbial community composition in lake water was significantly(P=0.001) correlated with geographic distance, salinity, and pH. Statistical analyses based on neutral community and null models indicated that stochastic processes may play predominant roles in shaping the microbial biogeographic distribution patterns in the studied global lake waters. The dispersal-related stochasticity(e.g., homogenizing dispersal) exhibited a stronger influence on the distribution of microbial community in freshwater lakes than in saline lakes. Overall, this work expands our understanding of the impact of geographic distance, environmental conditions, and stochastic processes on microbial distribution in global lakes.
