Properties of solutions of stochastic differential equations driven by the G-Brownian motion

In this paper, we study the differentiability of solutions of stochastic differential equations driven by the $G$-Brownian motion with respect to the initial data and the parameter. In addition, the stability of solutions of stochastic differential equations driven by the $G$-Brownian motion is obtained

A Novel Stealthy Target Detection Based on Stratospheric Balloon-borne Positional Instability due to Random Wind

A novel detection for stealthy target model F-117A with a higher aspect vision is introduced by using Stratospheric Balloon-borne Bistatic system. The potential problem of proposed scheme is platform instability impacted on the balloon by external wind force. The flight control system is studied in detail under typical random process, which is defined by Dryden turbulence spectrum. To accurately detect the stealthy target model, a real Radar Cross Section (RCS) based on physical optics (PO) formulation is applied. The sensitivity of the proposed scheme has been improved due to increasing PO – scattering field of stealthy model with higher aspect angle comparing to the conventional ground -based system. Simulations demonstrate that the proposed scheme gives much higher location accuracy and reduces location errors

Mixing Rates of Random Walks with Little Backtracking

Many regular graphs admit a natural partition of their edge set into cliques of the same order such that each vertex is contained in the same number of cliques. In this paper, we study the mixing rate of certain random walks on such graphs and we generalize previous results of Alon, Benjamini, Lubetzky and Sodin regarding the mixing rates of non-backtracking random walks on regular graphs.Comment: 31 pages; to appear in the CRM Proceedings Series, published by the American Mathematical Society as part of the Contemporary Mathematics Serie

Fay-like identities of the Toda Lattice Hierarchy and its dispersionless limit

In this paper, we derive the Fay-like identities of tau function for the Toda lattice hierarchy from the bilinear identity. We prove that the Fay-like identities are equivalent to the hierarchy. We also show that the dispersionless limit of the Fay-like identities are the dispersionless Hirota equations of the dispersionless Toda hierarchy.Comment: 20 page