3,578 Results Found

In this study, we introduce and rigorously formalize the notion of (P, m)-superquadratic stochastic processes, representing a novel and far-reaching generalization of classical convex stochastic processes. By exploring their intrinsic structural char...

We outline and test a new methodology for genuine simulation of stochastic processes with any dependence structure and any marginal distribution. We reproduce time dependence with a generalized, time symmetric or asymmetric, moving-average scheme. Th...

This paper addresses the generalization of counting processes through the age formalism of Lévy Walks. Simple counting processes are introduced and their properties are analyzed: Poisson processes or fractional Poisson processes can be recovered as p...

The theory of stochastic processes is the prominent part of advanced probability theory and very influential in various mathematical models having randomness. One of the potential aspects is to investigate the stochastic convex processes. Working in...

This article is a study of vector-valued renewal-reward processes on ${\mathbb{R}}^d$. The jumps of the process are assumed to be independent and identically distributed nonnegative random vectors with mutually dependent components, each of which may be either dis...

In this paper, we study a new family of Gompertz processes, defined by the power of the homogeneous Gompertz diffusion process, which we term the powers of the stochastic Gompertz diffusion process. First, we show that this homogenous Gompertz diffus...

When studying the behaviour of complex dynamical systems, a statistical formulation can provide useful insights. In particular, information geometry is a promising tool for this purpose. In this paper, we investigate the information length for n-dime...

In order to manage spreadability for quantum stochastic processes, we study in detail the structure of the involved monoids acting on the index-set of all integers $\mathbb{Z}$ , that is that generated by left and right hand-side partial shifts, the monoid...

The stochastic and undetermined nature of longwall coal mining results from the complex interaction between geological-mining and technical-organizational factors. This interaction causes variability in key parameters of the production process. This...

We propose a definition of entropy for stochastic processes. We provide a reproducing kernel Hilbert space model to estimate entropy from a random sample of realizations of a stochastic process, namely functional data, and introduce two approaches to...

The intent of the current study is to explore convex stochastic processes within a broader context. We introduce the concept of unified stochastic processes to analyze both convex and non-convex stochastic processes simultaneously. We employ weighted...

In this paper, we study the dynamic risk measures for processes induced by backward stochastic differential equations driven by Teugel’s martingales associated with Lévy processes (BSDELs). The representation theorem for generators of BSDELs is provi...

This article investigates the spectral structure of the evolution operators associated with the statistical description of stochastic processes possessing finite propagation velocity. Generalized Poisson–Kac processes and Lévy walks are...

This paper establishes a general parametric integral identity involving $(\mathfrak{n}+1)$-times differentiable stochastic processes, formulated entirely in terms of stochastic k-Caputo fractional derivatives. This identity serves as a unifying tool for deriving...

We use the definition of statistical symmetry as the invariance of a probability distribution under a given transformation and apply the concept to the underlying probability distribution of stochastic processes. To measure the degree of statistical...

This study presents, for the first time, a new class of interval-valued superquadratic stochastic processes and examines their core properties through the lens of the center-radius total order relation on intervals. These processes serve as a powerfu...

We consider linearizing transformations of the one-dimensional nonlinear stochastic differential equations driven by Wiener and compound Poisson processes, namely finite activity Levy processes. We present linearizability criteria and derive the requ...

In this study, we compare the performance of stochastic processes, namely, the Vasicek, Cox–Ingersoll–Ross (CIR), and geometric Brownian motion (GBM) models, with that of machine learning algorithms, such as Random Forest, Support Vector...

Many dynamical systems consist of multiple, co-evolving subsystems (i.e., they have multiple degrees of freedom). Often, the dynamics of one or more of these subsystems will not directly depend on the state of some other subsystems, resulting in a ne...

To implement the quality-relevant monitoring scheme for batch processes with multiple output modes, this paper presents a novel methodology based on stochastic programming. Bringing together tools from stochastic programming and ensemble learning, th...

The generation of synthetic time series is important in contemporary water sciences for their wide applicability and ability to model environmental uncertainty. Hydroclimatic variables often exhibit highly skewed distributions, intermittency (that is...

The Chemical Master Equation is a standard approach to model biochemical reaction networks. It consists of a system of linear differential equations, in which each state corresponds to a possible configuration of the reaction system, and the solution...

Stormwater quality modeling remains one of the most challenging issues in urban hydrology today. The processes involved in contaminant generation and transport are very complex, with many associated uncertainties, including uncertainty arising from p...

A set of core features is set forth as the essence of a thermodynamic description, which derive from large-deviation properties in systems with hierarchies of timescales, but which are not dependent upon conservation laws or microscopic reversibility...

The arrival of tracers at boundaries with defined distances from the origin of their motion in stochastically fluctuating advection processes is investigated. The advection model is a stationary one-dimensional integrated stochastic process with an a...

This paper is aimed at developing a stochastic volatility model that is useful to explain the dynamics of the returns of gold, silver, and platinum during the period 1994–2019. To this end, it is assumed that the precious metal returns are driven by...

The introduction of non-conventional energy sources (NCES) to industrial processes is a viable alternative to reducing the energy consumed from the grid. However, a robust coordination of the local energy resources with the power imported from the di...

Stochastic simulation has a prominent position in a variety of scientific domains including those of environmental and water resources sciences. This is due to the numerous applications that can benefit from it, such as risk-related studies. In such...

In gas-to-methanol processes, optimizing multi-energy systems is a critical challenge toward efficient energy allocation. This paper proposes an entropy-based stochastic optimization method for a multi-energy system in a gas-to-methanol process, aimi...

Random terms in many natural and social science systems have distinct Markovian characteristics, such as Markov jump-taking values in a finite or countable set, and Wiener process-taking values in a continuous set. In general, these systems can be se...

Existing neural stochastic differential equation models, such as SDE-Net, can quantify the uncertainties of deep neural networks (DNNs) from a dynamical system perspective. SDE-Net is either dominated by its drift net with in-distribution (ID) data t...

Sedimentary microorganisms play crucial roles in maintaining the functional stability of aquatic ecosystems. However, their taxonomic composition and assembly processes are not well known in estuarine–coastal margins because of their complex en...

By assimilating biological systems, both structural and functional, into multifractal objects, their behavior can be described in the framework of the scale relativity theory, in any of its forms (standard form in Nottale’s sense and/or the form of t...

Autonomous exploration of environmental fields is one of the most promising tasks to be performed by fleets of mobile underwater robots. The goal is to maximize the information gain during the exploration process by integrating an information-metric...

Convergence of a stochastic process is an intrinsic property quite relevant for its successful practical for example for the function optimization problem. Lyapunov functions are widely used as tools to prove convergence of optimization procedures. H...

The article proposes an approach to ensuring the functioning of Software-Defined Networks (SDN) in cyber attack conditions based on the analytical modeling of cyber attacks using the method of topological transformation of stochastic networks. Unlike...

We review the basics of fractal calculus, define fractal Fourier transformation on thin Cantor-like sets and introduce fractal versions of Brownian motion and fractional Brownian motion. Fractional Brownian motion on thin Cantor-like sets is defined...

In this paper, we introduce a spread model using multi-type branching processes to investigate the evolution of the population during a pandemic in which individuals are classified into different types. We study some limiting behaviors of the populat...

An infinite sequence $x_1{x}_2\dots$...

In this work, we consider dynamical systems of linear and nonlinear stochastic delay-differential equations driven by the Rosenblatt process. With the aid of the delayed matrix functions of these systems, we derive the controllability results as an a...

This paper explores a high-dimensional stochastic SIS epidemic model characterized by a mean-reverting, stochastic process. Firstly, we establish the existence and uniqueness of a global solution to the stochastic system. Additionally, by constructin...

In this work, we consider linear and nonlinear fractional stochastic delay systems driven by the Rosenblatt process. With the aid of the delayed Mittag-Leffler matrix functions and the representation of solutions of these systems, we derive the contr...

Stochastic models play a crucial role in global navigation satellite systems (GNSS) data processing. Many studies contribute to the stochastic modeling of GNSS observation noise, whereas few studies focus on the stochastic modeling of process noise....

In this paper, we study the one-dimensional homogeneous stochastic Brennan–Schwartz diffusion process. This model is a generalization of the homogeneous lognormal diffusion process. What is more, it is used in various contexts of financial math...

We study Mittag–Leffler (ML) fractional integrals involved in the solution processes of a system of coupled fractional stochastic differential equations. We introduce the ML fractional stochastic process as a ML fractional stochastic integral w...

Mathematical programming and optimization problems related to fluid dynamics are heavily influenced by stochastic processes associated with integral and variational inequalities. Furthermore, symmetry and convexity are intrinsically related. Over the...

It is known that, in quantum theory, measurements may suppress Hamiltonian dynamics of a system. A famous example is the ‘Quantum Zeno Effect’. This is the phenomena that, if one performs the measurements M times asking whether the system...

Stochastic processes are foundational tools in many scientific disciplines, including biology, operational research, social sciences, and stochastic finance, among others [...]

The stochastic (2+1)-dimensional breaking soliton equation (SBSE) is considered in this article, which is forced by the Wiener process. To attain the analytical stochastic solutions such as the polynomials, hyperbolic and trigonometric functions of t...

In this paper, we investigate the optimal control problems for a class of neutral stochastic integrodifferential equations (NSIDEs) with infinite delay driven by Poisson jumps and the Rosenblat process in Hilbert space involving concrete-fading memor...