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This paper introduces consensus-based primal-dual methods for distributed online optimization where the time-varying system objective function $f_t(\mathbf{x})$ is given as the sum of local agents' objective functions, i.e.,…
This paper studies the dividend and capital injection problem under a diffusion risk model with general discount functions. A proportional cost is imposed when injecting capitals. For exponential discounting as time-consistent benchmark, we…
Motivated by the current fears of a potentially stagflationary global economic environment, this paper uses new and recently introduced mathematical techniques to study multivariate time series pertaining to country inflation (CPI),…
The paper deals with a generalization of the risk model with stochastic premiums where dependence structures between claim sizes and inter-claim times as well as premium sizes and inter-premium times are modeled by…
Narrow escape and narrow capture problems which describe the average times required to stop the motion of a randomly travelling particle within a domain have applications in various areas of science. While for general domains, it is known…
Probability distributions having power-law tails are observed in a broad range of social, economic, and biological systems. We describe here a potentially useful common framework. We derive distribution functions $\{p_k\}$ for situations in…
In principle, the generalized master equation can be used to efficiently compute the macroscopic first passage time (FPT) distribution of a complex stochastic system from short-term microscopic simulation data. However, computing its…
A generalized Gaussian process model (GGPM) is a unifying framework that encompasses many existing Gaussian process (GP) models, such as GP regression, classification, and counting. In the GGPM framework, the observation likelihood of the…
We study the regret minimization problem in the novel setting of generalized kernelized bandits (GKBs), where we optimize an unknown function $f^*$ belonging to a reproducing kernel Hilbert space (RKHS) having access to samples generated by…
Predictability of behavior has emerged an an important characteristic in many fields including biology, medicine, and marketing. Behavior can be recorded as a sequence of actions performed by an individual over a given time period. This…
In studies of recurrent events, joint modeling approaches are often needed to allow for potential dependent censoring by a terminal event such as death. Joint frailty models for recurrent events and death with an additional dependence…
We discuss a family of models expressed by nonlinear differential equation systems describing closed market societies in the presence of taxation and redistribution. We focus in particular on three example models obtained in correspondence…
Regulatory requirements dictate that financial institutions must calculate risk capital (funds that must be retained to cover future losses) at least annually. Procedures for doing this have been well-established for many years, but recent…
Humans can learn several tasks in succession with minimal mutual interference but perform more poorly when trained on multiple tasks at once. The opposite is true for standard deep neural networks. Here, we propose novel computational…
The standard wage Phillips curve aggregates away from which workers reset wages when. I show this aggregation omits a first-order term: the covariance between workers' cost-push exposure and their reset frequency. I introduce two sufficient…
In this paper we consider a Bayesian framework for making inferences about dynamical systems from ergodic observations. The proposed Bayesian procedure is based on the Gibbs posterior, a decision theoretic generalization of standard…
Estimating the probabilistic Worst-Case Execution Time (pWCET) is essential for ensuring the timing correctness of real-time applications, such as in robot IoT systems and autonomous driving systems. While methods based on Extreme Value…
Many probabilistic inference problems such as stochastic filtering or the computation of rare event probabilities require model analysis under initial and terminal constraints. We propose a solution to this bridging problem for the widely…
A key aspect for any greedy pursuit algorithm used in compressed sensing is a good support-set detection method. For distributed compressed sensing, we consider a setup where many sensors measure sparse signals that are correlated via the…
We study an agent-based model of evolution of wealth distribution in a macro-economic system. The evolution is driven by multiplicative stochastic fluctuations governed by the law of proportionate growth and interactions between agents. We…