We study a stochastic differential equation with an unbounded drift and general Hölder continuous noise of order $\lambda \in (0,1)$. The corresponding equation turns out to have a unique solution that, depending on a particular shape of the drift, either stays above some continuous function or has continuous upper and lower bounds. Under some mild assumptions on the noise, we prove that the solution has moments of all orders. In addition, we provide its connection to the solution of some Skorokhod reflection problem. As an illustration of our results and motivation for applications, we also suggest two stochastic volatility models which we regard as generalizations of the CIR and CEV processes. We complete the study by providing a numerical scheme for the solution.

This paper deals with ergodic theorems for particular time-inhomogeneous Markov processes, whose time-inhomogeneity is asymptotically periodic. Under a Lyapunov/minorization condition, it is shown that, for any measurable bounded function f, the time average $\frac{1}{t} \int_0^t f(X_s)ds$ converges in $\mathbb{L}^2$ towards a limiting distribution, starting from any initial distribution for the process $(X_t)_{t \geq 0}$. This convergence can be improved to an almost sure convergence under an additional assumption on the initial measure. This result is then applied to show the existence of a quasi-ergodic distribution for processes absorbed by an asymptotically periodic moving boundary, satisfying a conditional Doeblin condition.

To describe the trend of cumulative incidence of coronavirus disease 19 (COVID-19) and undiagnosed cases over the pandemic through the emergence of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) variants among healthcare workers in Tokyo, we analysed data of repeated serological surveys and in-house COVID-19 registry among the staff of National Center for Global Health and Medicine. Participants were asked to donate venous blood and complete a survey questionnaire about COVID-19 diagnosis and vaccine. Positive serology was defined as being positive on Roche or Abbott assay against SARS-CoV-2 nucleocapsid protein, and cumulative infection was defined as either being seropositive or having a history of COVID-19. Cumulative infection has increased from 2.0% in June 2021 (pre-Delta) to 5.3% in December 2021 (post-Delta). After the emergence of the Omicron, it has increased substantially during 2022 (16.9% in June and 39.0% in December). As of December 2022, 30% of those who were infected in the past were not aware of their infection. Results indicate that SARS-CoV-2 infection has rapidly expanded during the Omicron-variant epidemic among healthcare workers in Tokyo and that a sizable number of infections were undiagnosed.

Two-part framework and the Tweedie generalized linear model (GLM) have traditionally been used to model loss costs for short-term insurance contracts. For most portfolios of insurance claims, there is typically a large proportion of zero claims that leads to imbalances, resulting in lower prediction accuracy of these traditional approaches. In this article, we propose the use of tree-based methods with a hybrid structure that involves a two-step algorithm as an alternative approach. For example, the first step is the construction of a classification tree to build the probability model for claim frequency. The second step is the application of elastic net regression models at each terminal node from the classification tree to build the distribution models for claim severity. This hybrid structure captures the benefits of tuning hyperparameters at each step of the algorithm; this allows for improved prediction accuracy, and tuning can be performed to meet specific business objectives. An obvious major advantage of this hybrid structure is improved model interpretability. We examine and compare the predictive performance of this hybrid structure relative to the traditional Tweedie GLM using both simulated and real datasets. Our empirical results show that these hybrid tree-based methods produce more accurate and informative predictions.

We present an efficient algorithm to generate a discrete uniform distribution on a set of p elements using a biased random source for p prime. The algorithm generalizes Von Neumann’s method and improves the computational efficiency of Dijkstra’s method. In addition, the algorithm is extended to generate a discrete uniform distribution on any finite set based on the prime factorization of integers. The average running time of the proposed algorithm is overall sublinear: $\operatorname{O}\!(n/\log n)$.

Multilayer networks are in the focus of the current complex network study. In such networks, multiple types of links may exist as well as many attributes for nodes. To fully use multilayer—and other types of complex networks in applications, the merging of various data with topological information renders a powerful analysis. First, we suggest a simple way of representing network data in a data matrix where rows correspond to the nodes and columns correspond to the data items. The number of columns is allowed to be arbitrary, so that the data matrix can be easily expanded by adding columns. The data matrix can be chosen according to targets of the analysis and may vary a lot from case to case. Next, we partition the rows of the data matrix into communities using a method which allows maximal compression of the data matrix. For compressing a data matrix, we suggest to extend so-called regular decomposition method for non-square matrices. We illustrate our method for several types of data matrices, in particular, distance matrices, and matrices obtained by augmenting a distance matrix by a column of node degrees, or by concatenating several distance matrices corresponding to layers of a multilayer network. We illustrate our method with synthetic power-law graphs and two real networks: an Internet autonomous systems graph and a world airline graph. We compare the outputs of different community recovery methods on these graphs and discuss how incorporating node degrees as a separate column to the data matrix leads our method to identify community structures well-aligned with tiered hierarchical structures commonly encountered in complex scale-free networks.