Accurate terrain estimation is critical for autonomous offroad navigation. Reconstruction of a 3D surface allows rough and hilly ground to be represented, yielding faster driving and better planning and control. However, data from a 3D sensor samples the terrain unevenly, quickly becoming sparse at longer ranges and containing large voids because of occlusions and inclines. The proposed approac...

We provide a unified treatment of pathwise Large and Moderate deviations principles for general class multidimensional stochastic Volterra equations with singular kernels, not necessarily convolution form. Our methodology is based on the weak convergence approach by Budhijara, Dupuis Ellis. show in particular how this framework encompasses most rough volatility models used mathematical finance ...

* Correspondence: yanpingch@126. com Department of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China Full list of author information is available at the end of the article Abstract Let 1 < p <∞ and n ≥ 2. The authors establish the L(R) boundedness for a class of parabolic singular integral operators with rough kernels. MR...

We consider large systems of particles interacting through rough but bounded interaction kernels. We are able to control the relative entropy between the N-particle distribution and the expected limit which solves the corresponding Vlasov system. This implies the Mean Field limit to the Vlasov system together with Propagation of Chaos through the strong convergence of all the marginals. The met...

Accurate terrain estimation is critical for autonomous offroad navigation. Reconstruction of a 3D surface allows rough and hilly ground to be represented, yielding faster driving and better planning and control. However, data from a 3D sensor samples the terrain unevenly, quickly becoming sparse at longer ranges and containing large voids because of occlusions and inclines. The proposed approac...

The Meda inequality for rearrangements of the convolution operator on the Heisenberg group Hn is proved. By using the Meda inequality, an O’Neil-type inequality for the convolution is obtained. As applications of these results, some sufficient and necessary conditions for the boundedness of the fractional maximal operator MΩ,α and fractional integral operator IΩ,α with rough kernels in the spac...