Existence and uniqueness results of the solution to fully coupled forward-backward stochastic defferential equations with Brownian motion and Poisson process are obtained. Many stochastic Hamilton systems arising in s...Existence and uniqueness results of the solution to fully coupled forward-backward stochastic defferential equations with Brownian motion and Poisson process are obtained. Many stochastic Hamilton systems arising in stochastic optimal control systems with random jump and in mathemstical finance with security price discontinuously changing can be treated with these results. The continuity of the solution depending on parameters is also proved in this paper.展开更多
During environment testing, the estimation of random vibration signals （RVS） is an important technique for the airborne platform safety and reliability. However, the available meth- ods including extreme value envel...During environment testing, the estimation of random vibration signals （RVS） is an important technique for the airborne platform safety and reliability. However, the available meth- ods including extreme value envelope method （EVEM）, statistical tolerances method （STM） and improved statistical tolerance method （ISTM） require large samples and typical probability distri- bution. Moreover, the frequency-varying characteristic of RVS is usually not taken into account. Gray bootstrap method （GBM） is proposed to solve the problem of estimating frequency-varying RVS with small samples. Firstly, the estimated indexes are obtained including the estimated inter- val, the estimated uncertainty, the estimated value, the estimated error and estimated reliability. In addition, GBM is applied to estimating the single flight testing of certain aircraft. At last, in order to evaluate the estimated performance, GBM is compared with bootstrap method （BM） and gray method （GM） in testing analysis. The result shows that GBM has superiority for estimating dynamic signals with small samples and estimated reliability is proved to be 100% at the given confidence level.展开更多
文摘Existence and uniqueness results of the solution to fully coupled forward-backward stochastic defferential equations with Brownian motion and Poisson process are obtained. Many stochastic Hamilton systems arising in stochastic optimal control systems with random jump and in mathemstical finance with security price discontinuously changing can be treated with these results. The continuity of the solution depending on parameters is also proved in this paper.
基金supported by Aviation Science Foundation of China (No. 20100251006)the Technological Foundation Project (No. J132012C001)
文摘During environment testing, the estimation of random vibration signals （RVS） is an important technique for the airborne platform safety and reliability. However, the available meth- ods including extreme value envelope method （EVEM）, statistical tolerances method （STM） and improved statistical tolerance method （ISTM） require large samples and typical probability distri- bution. Moreover, the frequency-varying characteristic of RVS is usually not taken into account. Gray bootstrap method （GBM） is proposed to solve the problem of estimating frequency-varying RVS with small samples. Firstly, the estimated indexes are obtained including the estimated inter- val, the estimated uncertainty, the estimated value, the estimated error and estimated reliability. In addition, GBM is applied to estimating the single flight testing of certain aircraft. At last, in order to evaluate the estimated performance, GBM is compared with bootstrap method （BM） and gray method （GM） in testing analysis. The result shows that GBM has superiority for estimating dynamic signals with small samples and estimated reliability is proved to be 100% at the given confidence level.
