相关论文: COGARCH: Symbol, Generator and Characteristics

In this paper, we present the principal components of an economic scenario generator (ESG), both for the theoretical design and for practical implementation. The choice of these components should be linked to the ultimate vocation of the…

We explain the algebra needed to make sense of the log signature of a path, with plenty of examples. We show how the log signature can be calculated numerically, and explain some software tools which demonstrate it.

We propose a coalgebraic model for constructing and reasoning about state-based protocols that implement efficient reductions among random processes. We provide basic tools that allow efficient protocols to be constructed in a compositional…

We investigate the concatenation of Markov processes. Our primary concern is to utilize processes constructed in this manner for Monte Carlo integration. To enable this using conventional methods, it is essential to demonstrate the Markov…

Background. It is assumed that the introduction of stochastic in mathematical model makes it more adequate. But there is virtually no methods of coordinated (depended on structure of the system) stochastic introduction into deterministic…

In context of highly complex energy system experiments, sensitivity analysis is gaining more and more importance to investigate the effects changing parameterization has on the outcome. Thus, it is crucial how to design an experiment to…

This paper introduces a novel Ito diffusion process to model high-frequency financial data, which can accommodate low-frequency volatility dynamics by embedding the discrete-time non-linear exponential GARCH structure with log-integrated…

Discovery of novel and promising materials is a critical challenge in the field of chemistry and material science, traditionally approached through methodologies ranging from trial-and-error to machine learning-driven inverse design. Recent…

In this study, ChatGPT is utilized to create streamlined models that generate easily interpretable features. These features are then used to evaluate financial outcomes from earnings calls. We detail a training approach that merges…

For systems that involve particle production through branching processes the concept of chaos is explored. The measures that can describe their behaviors are investigated. Monte Carlo simulation is used to generate events according to…

Identifying governing equations for a dynamical system is a topic of critical interest across an array of disciplines, from mathematics to engineering to biology. Machine learning -- specifically deep learning -- techniques have shown their…

We introduce stochastic and quantum finite-state transducers as computation-theoretic models of classical stochastic and quantum finitary processes. Formal process languages, representing the distribution over a process's behaviors, are…

Instrumental variable methods are often used for parameter estimation in the presence of confounding. They can also be applied in stochastic processes. Instrumental variable analysis exploits moment equations to obtain estimators for causal…

Mathematics can help analyze the arts and inspire new artwork. Mathematics can also help make transformations from one artistic medium to another, considering exceptions and choices, as well as artists' individual and unique contributions.…

Symbolic regression is a machine learning method with the goal to produce interpretable results. Unlike other machine learning methods such as, e.g. random forests or neural networks, which are opaque, symbolic regression aims to model and…

Gaussian processes are a natural way of defining prior distributions over functions of one or more input variables. In a simple nonparametric regression problem, where such a function gives the mean of a Gaussian distribution for an…

In this paper, we provide proofs for the analytic characterization theorems of the operator symbols utilizing the characterization theorem for the Mittag-Leffler distribution space.We work out examples which can be interpreted as integral…

We present a formalization of the OSGi component framework. Our formalization is intended to be used as a basis for describing behavior of OSGi based systems. Furthermore, we describe specification formalisms for describing properties of…

Regression analysis is used for prediction and to understand the effect of independent variables on dependent variables. Symbolic regression (SR) automates the search for non-linear regression models, delivering a set of hypotheses that…

We are going to study properties of "hypergeometrization" -- an operator which act on analytic functions near the origin by inserting two Pochhammer symbols into their Taylor series. In essence, this operator maps elementary function into…