Abstract Tropospheric correction models are receiving increasing attentions, as they play a crucial role in Global Navigation Satellite System (GNSS). Most commonly used models to date include the GPT2 series and the TropGrid2. In this study, we analyzed the advantages and disadvantages of existing models and developed a new model called the Improved Tropospheric Grid (ITG). ITG considers annual, semi-annual and diurnal variations and includes multiple tropospheric parameters. The amplitude and initial phase of diurnal variation are estimated as a periodic function. ITG provides temperature, pressure, the weighted mean temperature (Tm) and Zenith Wet Delay (ZWD). We conducted a performance comparison among the proposed ITG model and previous ones, in terms of meteorological measurements from 698 observation stations, Zenith Total Delay (ZTD) products from 280 International GNSS Service (IGS) station and Tm from Global Geodetic Observing System (GGOS) products. Results indicate that ITG offers the best performance on the whole.
We consider a general formulation of the random horizon Principal-Agent problem with a continuous payment and a lump-sum payment at termination. In the European version of the problem, the random horizon is chosen solely by the principal with no other possible action from the agent than exerting effort on the dynamics of the output process. We also consider the American version of the contract, which covers the seminal Sannikov's model, where the agent can also quit by optimally choosing the termination time of the contract. Our main result reduces such non-zero-sum stochastic differential games to appropriate stochastic control problems which may be solved by standard methods of stochastic control theory. This reduction is obtained by following Sannikov's approach, further developed by Cvitanic, Possamai, and Touzi. We first introduce an appropriate class of contracts for which the agent's optimal effort is immediately characterized by the standard verification argument in stochastic control theory. We then show that this class of contracts is dense in an appropriate sense so that the optimization over this restricted family of contracts represents no loss of generality. The result is obtained by using the recent well-posedness result of random horizon second-order backward SDE.
This paper deals with how to compute a nontrivial element efficiently in the kernel of a given structured matrix by parallel algorithm. This parallel algorithm is using the displacement rank method of a structured matrix with the computational complexity O(αn).
The main problem considered in this paper is how to find efficiently a nonzero element in the kernel of a given structured matrix with displacement approach by using O(αmn) basic operations.
The theory of backward SDEs extends the predictable representation property of Brownian motion to the nonlinear framework, thus providing a path-dependent analog of fully nonlinear parabolic PDEs. In this paper, we consider backward SDEs, their reflected version, and their second-order extension, in the context where the final data and the generator satisfy $L^1$-type of integrability condition. Our main objective is to provide the corresponding existence and uniqueness results for general Lipschitz generators. The uniqueness holds in the so-called Doob class of processes, simultaneously under an appropriate class of measures. We emphasize that the previous literature only deals with backward SDEs, and requires either that the generator is separable in $(y,z)$, see Peng [Pen97], or strictly sublinear in the gradient variable $z$, see [BDHPS03], or that the final data satisfies an $L\ln L$-integrability condition, see [HT18]. We by-pass these conditions by defining $L^1$-integrability under the nonlinear expectation operator induced by the previously mentioned class of measures.
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