Riemann-Liouville processes arising from Branching particle systems

It is proved in this paper that Riemann-Liouville processes can arise from the temporal structures of the scaled occupation time fluctuation limits of the site-dependent (d,\alpha,\sigma(x))branching particle systems in the case of 1=d<\alpha<2 and \int_{\R}\sigma(x)\d x<\infty.Comment: 12 page

The impact of cultural diversity and economic growth on the equalization of public cultural services——Empirical test based on spatial econometric model

The 13th Five Year Plan of the National Basic Public Service System plays an important role in promoting the equalization of basic public services in urban and rural areas. Based on the panel data of 242 prefecture level cities in 30 provinces of China from 2008 to 2018, this paper uses the spatial econometric model for empirical analysis. The study finds that the direct effect of cultural diversity on the equalization of public cultural services is negative and significant, that is, cultural diversity hinders the equalization of public cultural services in the region; the overall effect of economic growth on the equalization of public cultural services is positive and significant, and economic growth is indeed conducive to the promotion of public cultural services equal development in the region. Based on this, it is proposed that local governments should establish a differentiated supply system of public cultural products to effectively integrate local cultural resources, talents, volunteers and social organizations. We will increase financial investment in public cultural services and use government purchases to promote the gradual equalization of public cultural services in rural areas, border ethnic areas and urban rural fringe areas

Large and moderate deviations of weak record numbers in random walks

Record numbers are basic statistics in random walks, whose deviation principles are not very clear so far. In this paper, the asymptotic probabilities of large and moderate deviations for numbers of weak records in right continuous or left continuous random walks are proved.Comment: 17 pages. arXiv admin note: substantial text overlap with arXiv:1909.0976

Large and moderate deviations for record numbers in some non-nearest neighbor random walks

The deviation principles of record numbers in random walk models have not been completely investigated, especially for the non-nearest neighbor cases. In this paper, we derive the asymptotic probabilities of large and moderate deviations for the number of "weak records"(or "ladder points") in two kinds of one-dimensional non-nearest neighbor random walks. The proofs depend only on the direct analysis of random walks. We illustrate that the traditional method of analyzing the local time of Brownian motions, which is often adopted for the simple random walks, may not be optimal for our cases.Comment: 15 Page

Minimax Weight Learning for Absorbing MDPs

Reinforcement learning policy evaluation problems are often modeled as finite or discounted/averaged infinite-horizon MDPs. In this paper, we study undiscounted off-policy policy evaluation for absorbing MDPs. Given the dataset consisting of the i.i.d episodes with a given truncation level, we propose a so-called MWLA algorithm to directly estimate the expected return via the importance ratio of the state-action occupancy measure. The Mean Square Error (MSE) bound for the MWLA method is investigated and the dependence of statistical errors on the data size and the truncation level are analyzed. With an episodic taxi environment, computational experiments illustrate the performance of the MWLA algorithm.Comment: 36 pages, 9 figure

Non-conjugate boundary value problem of a third order differential equation

This paper is devoted to prove the existence of the optimal interval where the Green’s function is negative definite. The left and right endpoints of the interval are found. Then, a new principle of comparison of a third-order differential equation is established. As an application of our results, the solvability of a non-conjugate boundary value problem is discussed