Optimal probabilities and controls for reflecting diffusion processes

A solution to the optimal problem for determining vector fields which maximize (resp. minimize) the transition probabilities from one location to another for a class of reflecting diffusion processes is obtained in the present paper. The approach is based on a representation for the transition probability density functions. The optimal transition probabilities under the constraint that the drift vector field is bounded by a constant are studied in terms of the HJB equation. In dimension one, the optimal reflecting diffusion processes and the bang-bang diffusion processes are considered. We demonstrate by simulations that, even in this special case, the optimal diffusion processes exhibit an interesting feature of phase transitions. We also solve an optimal stochastic control problem for a class of stochastic control problems involving diffusion processes with reflection.Comment: 20 Pages, 2 figure

Explicit solutions for a class of nonlinear backward stochastic differential equations and their nodal sets

In this paper, we investigate a class of nonlinear backward stochastic differential equations (BSDEs) arising from financial economics, and give specific information about the nodal sets of the related solutions. As applications, we are able to obtain the explicit solutions to an interesting class of nonlinear BSDEs including the k-ignorance BSDE arising from the modeling of ambiguity of asset pricing

Anchor-Free Localization Method for Mobile Targets in Coal Mine Wireless Sensor Networks

Severe natural conditions and complex terrain make it difficult to apply precise localization in underground mines. In this paper, an anchor-free localization method for mobile targets is proposed based on non-metric multi-dimensional scaling (Multi-dimensional Scaling: MDS) and rank sequence. Firstly, a coal mine wireless sensor network is constructed in underground mines based on the ZigBee technology. Then a non-metric MDS algorithm is imported to estimate the reference nodes’ location. Finally, an improved sequence-based localization algorithm is presented to complete precise localization for mobile targets. The proposed method is tested through simulations with 100 nodes, outdoor experiments with 15 ZigBee physical nodes, and the experiments in the mine gas explosion laboratory with 12 ZigBee nodes. Experimental results show that our method has better localization accuracy and is more robust in underground mines

Direct structural identification of carbenium ions and investigation of host-guest interaction in the methanol to olefins reaction obtained by multinuclear NMR correlations

Probing and determining the intermediates formed during catalytic reactions in heterogeneous catalysis are strong challenges. Using C-13 labelling and two dimensional C-13-C-13 through-bond NMR correlations, we directly reveal the structures of a range of carbenium ion species formed during the conversion of methanol to olefins on acidic H-ZSM-5 zeolite by mapping the carbon-carbon bond connectivities. Additionally, we use C-13-Al-27 and Si-29-C-13 through-space NMR experiments to probe the interactions between the confined carbon species (including carbenium ions) and the framework of the zeolite, which quantitatively provide an estimate for the carbon-aluminium and carbon-silicon distances, respectively