Deterministic and stochastic effects drive the gut microbial diversity in cucurbit-feeding fruit flies (Diptera, Tephritidae). by Wouter Hendrycks, Nele Mullens, Jackline Bakengesa, Sija Kabota, Jenipher Tairo, Thierry Backeljau, Ramadhani Majubwa, Maulid Mwatawala, Marc De Meyer, Massimiliano Virgilio

“…We found that deterministic and stochastic processes play a considerable role in shaping the larval gut microbiome. …”
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Variable Exponent Function Spaces related to a Sublinear Expectation by Bochi Xu

“…A version of Kolmogorov’s criterion on variable exponent function spaces is proved for continuous modification of stochastic processes.…”
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Stochastic flows with interaction and measure-valued processes by Andrey A. Dorogovtsev

“…We consider the new class of the Markov measure-valued stochastic processes with constant mass. We give the construction of such processes with the family of the probabilities which describe the motion of single particles. …”
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On Quantum Statistical Mechanics: A Study Guide by Wladyslaw Adam Majewski

“…As an illustration, a quantization of stochastic processes, new formalism for statistical mechanics, quantum field theory, and quantum correlations are discussed.…”
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Random sums of random vectors and multitype families of productive individuals by I. Rahimov, H. Muttlak

“…Applying these limit theorems, we study the number of productive individuals in n-type indecomposable critical branching stochastic processes with types of individuals T1,…,Tn.…”
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Tracing microbial community across endophyte-to-saprotroph continuum of Cinnamomum camphora (L.) Presl leaves considering priority effect of endophyte on litter decomposition by Jiamin Xiao, Zaihua He, Xingbing He, Yonghui Lin, Xiangshi Kong

“…Bacterial community assembly was characterized by deterministic processes during the symbiotic phase, shifted to stochastic processes during the saprophytic phase. In contrast, fungal community assembly was predominantly driven by stochastic processes throughout the continuum. …”
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Comparative analysis of community composition and network structure between phyllosphere endophytic and epiphytic fungal communities of Mussaenda pubescens by Deqiang Chen, Juanjuan Yang, Shunfen Wang, Siren Lan, Yonglong Wang, Zhong-Jian Liu, Xin Qian

“…Crucially, the research indicates that stochastic processes play a substantial role in the composition of fungal communities. …”
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Non-Archimedean valued quasi-invariant descending at infinity measures by S. V. Lüdkovsky

“…Applications of such measures to pseudodifferential operators and stochastic processes are considered. Nevertheless, it is proved that there does not exist the complete non-Archimedean analog of Gaussian measures. …”
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Distinct ecological processes shape micro-eukaryotic generalists and specialists in a canal-disturbed wetland, Lake Weishan, China by Xinghao Li, Yunfeng Wang, Micah Dunthorn, Chengzhi Mao, Qiaoyi Kong, Saleh A. Al-Farraj, Weibo Song, Jie Huang

“…Notably, community assembly in this canal-disturbed lake was predominantly influenced by stochastic processes (58.18%) rather than deterministic processes (20.46%). …”
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Rough Paths above Weierstrass Functions by Cellarosi, Francesco, Selk, Zachary

“…The fundamental observation of rough paths theory is that if one can define “iterated integrals” above a signal, then one can construct solutions to differential equations driven by the signal.The typical examples of the signals of interest are stochastic processes such as (fractional) Brownian motion. …”
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Student Models for a Risky Asset with Dependence: Option Pricing and Greeks by Nikolai Leonenko, Anqi Liu, Nataliya Schestyuk

“…We summarize four models that construct stochastic processes of underlying prices with short-range and long-range dependencies. …”
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Weather forecast for simulation models of agroecosystem production by Eugenija Žiniauskaitė, Vitalijus Denisovas

“…The dynamics of main daily weather elements such as min and max daily temperatures, relative air humidity, cloudiness, precipitation and wind speed are described by discrete time stochastic processes. The first four elements are considered as the four-dimensional discrete time process while two others are modelled separately. …”
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Input-to-State Stability of Linear Stochastic Functional Differential Equations by Ramazan Kadiev, Arcady Ponosov

“…The purpose of the paper is to show how asymptotic properties, first of all stochastic Lyapunov stability, of linear stochastic functional differential equations can be studied via the property of solvability of the equation in certain pairs of spaces of stochastic processes, the property which we call input-to-state stability with respect to these spaces. …”
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The Sum and Difference of Two Lognormal Random Variables by C. F. Lo

“…By the Lie-Trotter operator splitting method, both the sum and difference are shown to follow a shifted lognormal stochastic process, and approximate probability distributions are determined in closed form. …”
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The role of multiple modeling perspectives in students' learning of exponential growth by Carlos Castillo-Garsow

“…The exponential is among the most important family functions in mathematics; the foundation for the solution of linear differential equations, linear difference equations, and stochastic processes. However there is little research and superficial agreement on how the concepts of exponential growth are learned and/or should be taught initially. …”
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Lyapunov Stability of the Generalized Stochastic Pantograph Equation by Ramazan Kadiev, Arcady Ponosov

“…To prove stability, we check that the solutions of the equation belong to a suitable space of stochastic processes, instead of searching for an appropriate Lyapunov functional. …”
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Convergence of weighted sums of independent random variables and an extension to Banach space-valued random variables by W. J. Padgett, R. L. Taylor

“…This extension provides a convergence theorem that applies to stochastic processes which may be considered as random elements in function spaces.…”
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Bacterial communities as bioindicators of climate change in freshwater ecosystems: Tank bromeliads as model systems by Daniel Di Pace Soares Penna, Gustavo Quevedo Romero, Mark P. Nessel, Angélica L. González, Valéria Maia Oliveira

“…However, the vulnerability of these rare species to stochastic processes raises concerns about community stability under climate change. …”
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A simple algorithm to generate firing times for leaky integrate-and-fire neuronal model by Aniello Buonocore, Luigia Caputo, Enrica Pirozzi, Maria Francesca Carfora

“…A method to generate first passage times for a class of stochastic processes is proposed. It does not require construction of the trajectories as usually needed in simulation studies, but is based on an integral equation whose unknown quantity is the probability density function of the studied first passage times and on the application of the hazard rate method. …”
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Fractional derivative in continuous-time Markov processes and applications to epidemics in networks by Matteo D'Alessandro, Piet Van Mieghem

“…We show that replacing the standard time derivative of the governing equation with a Caputo fractional derivative of order 0<α<1, leads to a fractional differential equation whose solution can describe the state probabilities of a class of non-Markovian stochastic processes. We show that the same state probabilities also solve a system of equations that describe semi-Markov processes in which the sojourn times follow a Mittag-Leffler distribution, contrasting the usual Markov processes with exponentially distributed sojourn times. …”
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