Estimating Remaining Useful Life for Degrading Systems with Large Fluctuations by Dang-Bo Du, Jian-Xun Zhang, Zhi-Jie Zhou, Xiao-Sheng Si, Chang-Hua Hu

“…Firstly the degradation data are decomposed into trend items and random items, which are defined as a stochastic process. Then the standard deviation of the stochastic process is defined as another performance variable because standard deviation reflects the system performance. …”
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Application of Discrete-time semi-Markov Model to the Stochastic forecasting of Capital assests as stock. by Nafiu, Lukman Abiodun, Patrick, Weke, Alieu Jallow, Mamadou, Carolyne, Ogutu

“…Semi Markov is a stochastic process that generalizes both the Markov chain and the Markov renewal processes. it is well known that the performances of the stock market or factors that move stock prices are technical factors, fundamental factors and market sentiments.…”
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Operator Inequalities of Morrey Spaces Associated with Karamata Regular Variation by Jiajia Wang, Zunwei Fu, Shaoguang Shi, Ling Mi

“…Karamata regular variation is a basic tool in stochastic process and the boundary blow-up problems for partial differential equations (PDEs). …”
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Analytic-Numerical Solution of Random Boundary Value Heat Problems in a Semi-Infinite Bar by M.-C. Casabán, J.-C. Cortés, B. García-Mora, L. Jódar

“…Using previous results about random ordinary differential equations, a closed form solution stochastic process is firstly obtained. Then, expectation and variance are computed. …”
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Option Pricing Based on Modified Advection-Dispersion Equation: Stochastic Representation and Applications by Longjin Lv, Luna Wang

“…In this paper, we first investigate the stochastic representation of the modified advection-dispersion equation, which is proved to be a subordinated stochastic process. Taking advantage of this result, we get the analytical solution and mean square displacement for the equation. …”
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Evolutionary dynamics of prey-predator systems with Holling type II functional response by Jian Zu, Wendi Wang, Bo Zu

“…The evolutionarydynamics is constructed from a stochastic process of mutation andselection. We investigate the ecological and evolutionary conditionsthat allow for continuously stable strategy and evolutionarybranching. …”
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A First Application of the Backward Technique in Social Sciences: Exploring Demographic Noise in a Model with Three Personality Types by Roberto Macrelli, Margherita Carletti, Vincenzo Fano

“…Applying the backward technique to this model built on ordinary differential equations, we demonstrate how demographic noise can act as a switching factor, i.e., moving backward from the deterministic continuous model to the discrete stochastic process using the same parameter values, a given equilibrium switches to a different one. …”
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The Long Time Behavior of Equilibrium Status of a Predator-Prey System with Delayed Fear in Deterministic and Stochastic Scenarios by Weili Kong, Yuanfu Shao

“…Next, by perturbing the mortality rates of prey species and predator species, we stretch the deterministic system to the stochastic scenario and investigate the existence of stochastic process and the global asymptotical stability of the equilibrium status. …”
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Effects of elongation delay in transcription dynamics by Xuan Zhang, Huiqin Jin, Zhuoqin Yang, Jinzhi Lei

“…This paper studies the transcription dynamics that involved the elongation delay and effects of cell division and DNA replication. The stochastic process of gene expression is modeled with delay chemical master equation with periodic coefficients, and is studied numerically through the stochastic simulation algorithm with delay. …”
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2019-nCoV Transmission in Hubei Province, China: Stochastic and Deterministic Analyses by Zhiming Li, Zhidong Teng, Changxing Ma

“…Under R0>1, quasi-stationary distribution of the stochastic process is approximated by Gaussian diffusion. …”
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Measuring Interest Rate Risk with Embedded Option Using HPL-MC Method in Fuzzy and Stochastic Environment by Enlin Tang, Wei Du

“…Under the premise that the fluctuation of interest rate follows fuzzy stochastic process, based on the option characteristics of financial instruments with embedded option, this paper takes effective duration and effective convexity as tools to measure interest rate risk when embedded options exist, tries to choose CIR extended model as term structure model, and uses the Monte Carlo method for hybrid low deviation sequences (HPL-MC) to analyze the prepayment characteristics of MBS, a representative financial instrument with embedded options, when interest rates fluctuate; on this basis, the effectiveness of effective duration management of interest rate risk is demonstrated with asset liability management cases of commercial banks.…”
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Optimal time to intervene: The case of measles child immunization by Zuzana Chladná

“…We represent immunization rate of newborns as a stochastic process and intervention as a one-period jump of this process. …”
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Stochastic Control of Inertial Sea Wave Energy Converter by Mattia Raffero, Michele Martini, Biagio Passione, Giuliana Mattiazzo, Ermanno Giorcelli, Giovanni Bracco

“…The response of the WEC (wave energy converter) is driven by the sea-surface elevation, which is modeled by a stationary and homogeneous zero mean Gaussian stochastic process. System equations are linearized thus simplifying the numerical model of the device. …”
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Evolution of Bounded Confidence Opinion in Social Networks by Hui Xie, Guangjian Li, Yongjie Yan, Sihui Shu

“…We investigate opinion dynamics as a stochastic process in social networks. We introduce the stubborn agent in order to determine the impact of network structure on the emergence of consensus. …”
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Measured Rare Voltage Sags and Clusters of Sags: Prediction Models Driven by the Intermittence Indices by G. M. Casolino, M. de Santis, L. Di Stasio, C. Noce, P. Varilone, P. Verde

“…The clusters of sags represent a stochastic process due to their time dependence; the rare satisfy the requirements for a Poisson distribution process. …”
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Evaluation Formulas for Generalized Conditional Wiener Integrals with Drift on a Function Space by Dong Hyun Cho

“…Let C[0,t] denote a generalized Wiener space, the space of real-valued continuous functions on the interval [0,t] and define a stochastic process Y:C[0,t]×[0,t]→ℝ by Y(x,s)=∫0s‍h(u)dx(u)+a(s) for x∈C[0,t] and s∈[0,t], where h∈L2[0,t] with h≠0 a.e. and a is continuous on [0,t]. …”
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Markov Switching Model Analysis of Implied Volatility for Market Indexes with Applications to S&P 500 and DAX by Luca Di Persio, Samuele Vettori

“…In particular the volatility parameter is treated as an unobserved state variable whose value in time is given as the outcome of an unobserved, discrete-time and discrete-state, stochastic process represented by a suitable Markov chain. …”
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A Statistical Channel Model for Stochastic Antenna Inclination Angles by Gang Liu, Ming Zhang, Yaming Bo

“…The actions of a person holding a mobile device are not a static state but can be considered as a stochastic process since users can change the way they hold the device very frequently in a short time. …”
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Gene function revealed at the moment of stochastic gene silencing by Shreyan Gupta, James J. Cai

“…Abstract Gene expression is a dynamic and stochastic process characterized by transcriptional bursting followed by periods of silence. …”
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Analogues of Conditional Wiener Integrals with Drift and Initial Distribution on a Function Space by Dong Hyun Cho

“…Let C[0,T] denote a generalized Wiener space, the space of real-valued continuous functions on the interval [0,T], and define a stochastic process Z:C[0,T]×[0,T]→R by Z(x,t)=∫0t‍h(u)dx(u)+x(0)+a(t), for x∈C[0,T] and t∈[0,T], where h∈L2[0,T] with h≠0 a.e. and a is a continuous function on [0,T]. …”
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