Occupation Time Fluctuations of Weakly Degenerate Branching Systems

We establish limit theorems for re-scaled occupation time fluctuations of a sequence of branching particle systems in $\R^d$ with anisotropic space motion and weakly degenerate splitting ability. In the case of large dimensions, our limit processes lead to a new class of operator-scaling Gaussian random fields with non-stationary increments. In the intermediate and critical dimensions, the limit processes have spatial structures analogous to (but more complicated than) those arising from the critical branching particle system without degeneration considered by Bojdecki et al.{\it Stochastic Process. Appl. 2006}. Due to the weakly degenerate branching ability, temporal structures of the limit processes in all three cases are different from those obtained by Bojdecki et al. .{\it Stochastic Process. Appl. 2006}.Comment: 27page

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

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

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