For a given probability density function p（x） on R^d, we construct a （non-stationary） diffusion process xt, starting at any point x in R^d, such that 1/T ∫_o^T δ（xt-x）dt converges to p（x） almost surely. The ...For a given probability density function p（x） on R^d, we construct a （non-stationary） diffusion process xt, starting at any point x in R^d, such that 1/T ∫_o^T δ（xt-x）dt converges to p（x） almost surely. The rate of this convergence is also investigated. To find this rate, we mainly use the Clark-Ocone formula from Malliavin calculus and the Girsanov transformation technique.展开更多
Carbon-enriched lignocelluloses are regarded as the perfect alternative for nonrenewable fossil fuel, and have a great potential to alleviate the increasing energy crisis and climate change. However, the tightly coval...Carbon-enriched lignocelluloses are regarded as the perfect alternative for nonrenewable fossil fuel, and have a great potential to alleviate the increasing energy crisis and climate change. However, the tightly covalent structure and strong intra and in- ter-molecular hydrogen bonding in lignoceUulose make it high recalcitrance to transformation due to the poor solubility in wa- ter or common organic solvents. Dissolution and transformation of lignocellulose and its constituents in ionic liquids have therefore attracted much attention recently due to the tunable physical-chemical properties. Here, ionic liquids with excellent dissolving capability for biomass and its ingredients were examined. The technologies for lignocellulose biorefining in the presence of ionic liquid solvents or catalysts were also summarized. Some pertinent suggestions for the future catalytic conver- sion and unitization of this sustained carbon-rich resource are proposed.展开更多
基金supported by the Simons Foundation (Grant No. 209206)a General Research Fund of the University of Kansas
文摘For a given probability density function p（x） on R^d, we construct a （non-stationary） diffusion process xt, starting at any point x in R^d, such that 1/T ∫_o^T δ（xt-x）dt converges to p（x） almost surely. The rate of this convergence is also investigated. To find this rate, we mainly use the Clark-Ocone formula from Malliavin calculus and the Girsanov transformation technique.
基金financial support of the National Natural Science Foundation of China (20876055, 21076085)the Natural Science Foundation of Guangdong Province (S2011020001472)the Fundamental Research Funds for the Central Universities, SCUT
文摘Carbon-enriched lignocelluloses are regarded as the perfect alternative for nonrenewable fossil fuel, and have a great potential to alleviate the increasing energy crisis and climate change. However, the tightly covalent structure and strong intra and in- ter-molecular hydrogen bonding in lignoceUulose make it high recalcitrance to transformation due to the poor solubility in wa- ter or common organic solvents. Dissolution and transformation of lignocellulose and its constituents in ionic liquids have therefore attracted much attention recently due to the tunable physical-chemical properties. Here, ionic liquids with excellent dissolving capability for biomass and its ingredients were examined. The technologies for lignocellulose biorefining in the presence of ionic liquid solvents or catalysts were also summarized. Some pertinent suggestions for the future catalytic conver- sion and unitization of this sustained carbon-rich resource are proposed.
