The 𝒮-Transform of Sub-fBm and an Application to a Class of Linear Subfractional BSDEs by Zhi Wang, Litan Yan

“…As an application we study the solutions of backward stochastic differential equations driven by SH of the form -dYt=f(t,Yt,Zt)dt-ZtdStH, t∈[0,T],YT=ξ, where the stochastic integral used in the above equation is Pettis integral. …”
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About stability of equilibria of one system of stochastic delay differential equations with exponential nonlinearity by Leonid Shaikhet

“…The obtained results are illustrated via examples and figures with numerical simulations of solutions of a considered system of stochastic differential equations. The proposed way of investigation can be applied to nonlinear systems of higher dimension and with other types of nonlinearity, both for delay differential equations and for difference equations.…”
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Convergence Theorems for Operators Sequences on Functionals of Discrete-Time Normal Martingales by Jinshu Chen

“…Finally, we apply the results obtained here and establish the existence and uniqueness of solution to quantum stochastic differential equations in terms of operators acting on functionals of discrete-time normal martingales M. …”
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Optimal control via FBSDE with dynamic risk penalization: a structuring formulation based on Pontryagin's principle by Kayembe Tcheick, Mubenga Kamputo Pascal, Bofeki Bosonga, Eugene Mbuyi Mukendi

“…Leveraging Forward-Backward Stochastic Differential Equations (FBSDEs), our approach enables adaptive risk regulation in response to market fluctuations. …”
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Approximating Explicitly the Mean-Reverting CEV Process by N. Halidias, I. S. Stamatiou

“…We are interested in the numerical solution of mean-reverting CEV processes that appear in financial mathematics models and are described as nonnegative solutions of certain stochastic differential equations with sublinear diffusion coefficients of the form (xt)q, where 1/2<q<1. …”
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Evolution of momentum-dependent observables under stochastic phase noise in Rabi oscillations by Samuel Böhringer, Fabian Kienle, Richard Lopp

“…In particular, we show that such momentum-dependent observables evolve under stochastic differential equations (SDEs) in the form of geometrical Brownian motion and find that these SDEs reduce to ordinary differential equations (ODEs) for the expectation values under white laser phase noise. …”
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Robust Guaranteed Cost Observer Design for Singular Markovian Jump Time-Delay Systems with Generally Incomplete Transition Probability by Yanbo Li, Yonggui Kao, Jing Xie

“…Based on stability theory of stochastic differential equations and linear matrix inequality (LMI) technique, we design an observer to ensure that, for all uncertainties, the resulting augmented system is regular, impulse free, and robust stochastically stable with the proposed guaranteed cost performance. …”
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Asymptotic Behavior of a Stochastic Two-Species Competition Model under the Effect of Disease by Rong Liu, Guirong Liu

“…By the comparison theorem of stochastic differential equations, we prove the existence and uniqueness of global positive solution of the model. …”
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Modeling, Real-Time Estimation, and Identification of UWB Indoor Wireless Channels by Mohammed M. Olama, Seddik M. Djouadi, Yanyan Li, Aly Fathy

“…Stochastic differential equations (SDEs) are used to model ultrawideband (UWB) indoor wireless channels. …”
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Axial shear modulus of a fiber-reinforced composite with random fiber cross-sections by S. K. Bose, L. Debnath

“…A study is made of the effective axial shear modulus of a fiber reinforced material with random fiber cross-sections so that the micromechanics is governed by stochastic differential equations. A coarse-graining procedure is adopted to investigate the macroscopic behavior of the material. …”
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Exponential stability of a kind of stochastic delay difference equations by Xiaohua Ding

“…We present a Razumilchin-type theorem for stochastic delay difference equation, and use it to investigate the mean square exponential stability of a kind of nonautonomous stochastic difference equation which may also be viewed as an approximation of a nonautonomous stochastic delay integrodifferential equations (SDIDEs), and of a difference equation arises from some of the earliest mathematical models of the macroeconomic trade cycle with the environmental noise.…”
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DEVELOPING A MATHEMATICAL MODEL FOR THE PROCESS OF DEVELOPING A MATHEMATICAL MODEL FOR THE PROCESS OF SEDIMENTARY TANKS by Valeria Victoria IOVANOV

“…The model is reformulated by means of stochastic differential equations, and the parametersare estimated by a maximum likelihood method.VESILIND (1968; 1979) proposed a sludge settling velocity model of exponential form. …”
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Enhanced Squeezing and Entanglement in Nondegenerate Three-Level Laser Coupled to Squeezed Vacuum Reservoir by Ebisa Mosisa

“…I obtain stochastic differential equations associated with the normal ordering using the pertinent master equation. …”
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Resonance Mechanism of Nonlinear Vibrational Multistable Energy Harvesters under Narrow-Band Stochastic Parametric Excitations by Dongmei Huang, Shengxi Zhou, Zhichun Yang

“…To explore the stochastic bifurcation phenomenon between the nontrivial and trivial steady-state solutions, the Fokker–Planck–Kolmogorov equation corresponding to the two-dimensional Itô stochastic differential equations is solved by using the finite difference method. …”
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Exact controllability of rational expectations model with multiplicative noise and input delay by Wenjing Wang, Juanjuan Xu, Huanshui Zhang, Minyue Fu

“…The key is the solvability of the backward stochastic difference equations with input delay which is derived from the forward and backward stochastic system.…”
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A Case Study on Designing a Sliding Mode Controller to Stabilize the Stochastic Effect of Noise on Mechanical Structures: Residential Buildings Equipped with ATMD by Aydin Azizi

“…In this study, the ground motion is considered as a Wiener process, in which the governing stochastic differential equations have been presented in the form of Ito equation. …”
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Threshold dynamics of stochastic SIRSW infectious disease model with multiparameter perturbation by Zhengwen Yin, Yuanshun Tan

“…In addition to establishing the existence and uniqueness of the global positive solution of the model, we derived the threshold conditions for the extinction and persistence of the disease using the comparison theorem and It$ \hat{o} $'s formula of stochastic differential equations. Subsequently, we obtained the asymptotic stability of both the disease-free equilibrium and the endemic equilibrium of the deterministic model corresponding to the stochastic model through stochastic stability theory. …”
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Stabilizing role of multiplicative noise in nonconfining potentials by Ewan T. Phillips, Benjamin Lindner, Holger Kantz

“…We focus on a large class of one-dimensional stochastic differential equations in which the deterministic drift pushes trajectories toward infinity. …”
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Integrating Dynamical Systems Modeling with Spatiotemporal scRNA-Seq Data Analysis by Zhenyi Zhang, Yuhao Sun, Qiangwei Peng, Tiejun Li, Peijie Zhou

“…These technologies, when combined with computational frameworks such as Markov chains, stochastic differential equations (SDEs), and generative models like optimal transport and Schrödinger bridges, enable the reconstruction of dynamic cellular trajectories and cell fate decisions. …”
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Probabilistic Basin of Attraction and Its Estimation Using Two Lyapunov Functions by Skuli Gudmundsson, Sigurdur Hafstein

“…We study stability for dynamical systems specified by autonomous stochastic differential equations of the form dX(t)=f(X(t))dt+g(X(t))dW(t), with (X(t))t≥0 an Rd-valued Itô process and (W(t))t≥0 an RQ-valued Wiener process, and the functions f:Rd→Rd and g:Rd→Rd×Q are Lipschitz and vanish at the origin, making it an equilibrium for the system. …”
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