Estimating Speed and Damping in the Stochastic Wave Equation

Estimating the characteristics of stochastic damping Hamiltonian systems from continuous observations

We consider nonparametric invariant density and drift estimation for a class of multidimensional degenerate resp. hypoelliptic diffusion processes, so-called stochastic damping Hamiltonian systems or kinetic diffusions, under anisotropic smoothness assumptions on the unknown functions. The analysis is based on continuous observations of the process, and the estimators' performance is measured in terms of the sup-norm loss. Regarding invariant density estimation, we obtain highly nonclassical results for the rate of convergence, which reflect the inhomogeneous variance structure of the process.…

Speed of convergence in first passage percolation and geodesicity of the average distance

We give an elementary proof that Talagrand's sub-Gaussian concentration inequality implies a limit shape theorem for first passage percolation on any Cayley graph of Z^d, with a bound on the speed of convergence that slightly improves Alexander's bounds. Our approach, which does not use the subadditive theorem, is based on proving that the average distance is close to being geodesic. Our key observation, of independent interest, is that the problem of estimating the rate of convergence for the average distance is equivalent (in a precise sense) to estimating its "level of geodesicity".

在零回归连续时间马尔可夫链中估计首次返回速度

Estimation of First Returning Speed in Null Recurrent Continuous-Time Markov Chains

本文提出了一种基于电力网络理论的方法，用于估计零回归连续时间马尔可夫链的首次返回速度，并提供了相关示例。