Uniform Estimates for Eulerian-Lagrangian Methods for Singularly Perturbed Time-Dependent Problems

We prove a priori optimal-order error estimates in a weighted energy norm for several Eulerian–Lagrangian methods for singularly perturbed, time-dependent convection-diffusion equations with full regularity. The estimates depend only on certain Sobolev norms of the initial and right-hand side data, but not on ε or any norm of the true solution, and so hold uniformly with respect to ε. We use the interpolation of spaces and stability estimates to derive an ε-uniform estimate for problems with minimal or intermediate regularity, where the convergence rates are proportional to certain Besov norms of the initial and right-hand side data

Significant wave height forecasting based on the hybrid EMD-SVM method

1957-1962Prediction of significant wave height (SWH) is considered an effective method in marine engineering and prevention of marine disasters. Support vector machine (SVM) model has limitations in processing nonlinear and non-stationary SWH time series. Fortunately, empirical mode decomposition (EMD) can effectively deal with the complicated series. So, the SWH prediction method based on EMD and SVM is proposed by combining the advantages of both methods. A statistical analysis was carried out to compare the results of two models i.e., between the hybrid EMD-SVM and SVM. In addition, two models are used for forecasting SWH with 3, 6, 12 and 24 hours lead times, respectively. A high R value of different prediction times for the hybrid model. Results indicate that SWH prediction of the hybrid EMD-SVM model is superior to the SVM model

C-Procgen: Empowering Procgen with Controllable Contexts

We present C-Procgen, an enhanced suite of environments on top of the Procgen benchmark. C-Procgen provides access to over 200 unique game contexts across 16 games. It allows for detailed configuration of environments, ranging from game mechanics to agent attributes. This makes the procedural generation process, previously a black-box in Procgen, more transparent and adaptable for various research needs.The upgrade enhances dynamic context management and individualized assignments, while maintaining computational efficiency. C-Procgen's controllable contexts make it applicable in diverse reinforcement learning research areas, such as learning dynamics analysis, curriculum learning, and transfer learning. We believe that C-Procgen will fill a gap in the current literature and offer a valuable toolkit for future works

Optimal dividend and capital injection under spectrally positive Markov additive models

This paper studies De Finetti's optimal dividend problem with capital injection under spectrally positive Markov additive models. Based on dynamic programming principle, we first study an auxiliary singular control problem with a final payoff at an exponential random time. The double barrier strategy is shown to be optimal and the optimal barriers are characterized in analytical form using fluctuation identities of spectrally positive Levy processes. We then transform the original problem under spectrally positive Markov additive models into an equivalent series of local optimization problems with the final payoff at the regime-switching time. The optimality of the regime-modulated double barrier strategy can be confirmed for the original problem using results from the auxiliary problem and the fixed point argument for recursive iterations.Comment: Keywords: Spectrally positive Levy process, regime switching, De Finetti's optimal dividend, capital injection, double barrier strategy, singular contro

On De Finetti's control under Poisson observations: optimality of a double barrier strategy in a Markov additive model

In this paper we consider the De Finetti's optimal dividend and capital injection problem under a Markov additive model. We assume that the surplus process before dividends and capital injections follows a spectrally positive Markov additive process. Dividend payments are made only at the jump times of an independent Poisson process. Capitals are required to be injected whenever needed to ensure a non-negative surplus process to avoid bankruptcy. Our purpose is to characterize the optimal periodic dividend and capital injection strategy that maximizes the expected total discounted dividends subtracted by the total discounted costs of capital injection. To this end, we first consider an auxiliary optimal periodic dividend and capital injection problem with final payoff under a single spectrally positive L\'evy process and conjecture that the optimal strategy is a double barrier strategy. Using the fluctuation theory and excursion-theoretical approach of the spectrally positive L\'evy process and the Hamilton-Jacobi-Bellman inequality approach of the control theory, we are able to verify the conjecture that some double barrier periodic dividend and capital injection strategy solves the auxiliary problem. With the results for the auxiliary control problem and a fixed point argument for recursive iterations induced by the dynamic programming principle, the optimality of a regime-modulated double barrier periodic dividend and capital injection strategy is proved for our target control problem.Comment: arXiv admin note: text overlap with arXiv:2207.0266

Can the Black Lives Matter Movement Reduce Racial Disparities? Evidence from Medical Crowdfunding

Using high-frequency donation records from a major medical crowdfunding site and careful difference-in-difference analysis, we demonstrate that the 2020 BLM surge decreased the fundraising gap between Black and non-Black beneficiaries by around 50\%. The reduction is largely attributed to non-Black donors. Those beneficiaries in counties with moderate BLM activities were most impacted. We construct innovative instrumental variable approaches that utilize weekends and rainfall to identify the global and local effects of BLM protests. Results suggest a broad social movement has a greater influence on charitable-giving behavior than a local event. Social media significantly magnifies the impact of protests

The Adaptive Market Hypothesis：An empirical study on the UK stock market

This paper uses the FTSE 350 daily data and subsample method to detect the Adaptive Market Hypothesis (AMH) in the UK stock market. We performed a range of linear and nonlinear tests on sixteen two-yearly subsamples to capture the time-varying characteristic of market efficiency from 1987 to 2018. Both linear and nonlinear test results provide evidence that the market efficiency is not an all-or-nothing condition, and stock returns experience predictable and unpredictable periods. In addition, we find there is a downward trend for the January effect in the UK stock market during the sample period. Meanwhile, the analysis result suggests that AMH based on its more realistic assumptions provides a better explanation of the January effect than the Efficient Market Hypothesis

Robust Reinforcement Learning via Adversarial Kernel Approximation

Robust Markov Decision Processes (RMDPs) provide a framework for sequential decision-making that is robust to perturbations on the transition kernel. However, robust reinforcement learning (RL) approaches in RMDPs do not scale well to realistic online settings with high-dimensional domains. By characterizing the adversarial kernel in RMDPs, we propose a novel approach for online robust RL that approximates the adversarial kernel and uses a standard (non-robust) RL algorithm to learn a robust policy. Notably, our approach can be applied on top of any underlying RL algorithm, enabling easy scaling to high-dimensional domains. Experiments in classic control tasks, MinAtar and DeepMind Control Suite demonstrate the effectiveness and the applicability of our method