Approximate Controllability of Hilfer Fractional Stochastic Evolution Inclusions of Order 1 < q < 2 by Anurag Shukla, Sumati Kumari Panda, Velusamy Vijayakumar, Kamalendra Kumar, Kothandabani Thilagavathi

“…First, we explored the prospects of finding mild solutions for the Hilfer fractional stochastic differential equation. Subsequently, we determined that the specified system is approximately controllable. …”
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Catalyst: Fast and flexible modeling of reaction networks. by Torkel E Loman, Yingbo Ma, Vasily Ilin, Shashi Gowda, Niklas Korsbo, Nikhil Yewale, Chris Rackauckas, Samuel A Isaacson

“…Catalyst supports simulating stochastic chemical kinetics (jump process), chemical Langevin equation (stochastic differential equation), and reaction rate equation (ordinary differential equation) representations for CRNs. …”
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Time-Varying Reliability Analysis of Integrated Power System Based on Dynamic Bayesian Network by Jiacheng Wei, Tong Chen, Haolin Wen, Haobang Liu

“…By embedding a multi-physics coupled degradation model into the conditional probability nodes of the Dynamic Bayesian Network, a joint stochastic differential equation for the degradation process was constructed, and the dynamic correlation between continuous degradation and discrete fault events throughout the entire life cycle was achieved. …”
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A stochastic model for water-vegetation systems and the effect of decreasing precipitation on semi-arid environments by Shannon Dixon, Nancy Huntly, Priscilla E. Greenwood, Luis F. Gordillo

“…The model, a stochastic differential equation approximation derived from a Markov jump process, is used to generate extensive simulations that suggest a relationship between precipitation reduction and the desertification process, which might take several years in some instances.…”
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Dynamic Programming-Based Approach to Model Antigen-Driven Immune Repertoire Synthesis by Alexander S. Bratus, Gennady Bocharov, Dmitry Grebennikov

“…Optimal control synthesis is based on the solution of the Hamilton–Jacobi–Bellman equation implementing the dynamic programming approach for controlling Gaussian random processes generated by a stochastic differential equation (SDE) with the noise in the form of the Wiener process. …”
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Probabilistic Analysis of the Auto Tracking Failure by the Mobile Robot Video System by A. A. Lobaty, M. M. Tatur, A. K. Ibrahim

“…The mathematical formulation of the probabilistic analysis problem is based on the processes representation occurring in the system by a vector stochastic differential equation. The condition for the auto tracking failure is the exit of the tracked object from the of the video system field of view and non-return to it within a specified time. …”
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Feasibility of variable delay fuzzy fractional stochastic differential system with non-instantaneous impulses by Manjitha Mani Shalini, Banupriya Kandasamy, Maheswari Rangasamy, Prasantha Bharathi Dhandapani, Anwar Zeb, Ilyas Khan, Abdoalrahman S.A. Omer

“…Specifically, the paper introduces a new fractional stochastic differential equation (FSDE) featuring variable fuzzy delays and non-instantaneous impulses driven by FBM. …”
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Demographic consequences of damage dynamics in single-cell aging by Murat Tuğrul, Ulrich K. Steiner

“…Here, we present a generic and flexible damage model using a stochastic differential equation approach that incorporates stochastic damage accumulation and asymmetric damage partitioning during cell divisions. …”
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Asymptotic optimality of a joint scheduling–control policy for parallel server queues with multiclass jobs in heavy traffic by Xiaolong Li

“…This limit problem, which we call the diffusion control problem (DCP), is a stochastic differential equation (SDE). Next, we present the corresponding Hamilton–Jacobi–Bellman (HJB) equation and prove the existence and uniqueness of the solution to this equation. …”
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CATL's stock price forecasting and its derived option pricing: a novel extended fNSDE-net method by Xiao Qi, Tianyao Duan, Lihua Wang, Huan Guo

“…This paper presents a novel numerical method, named extended fractional neural stochastic differential equation (fNSDE)-Net, which combines the generative adversarial network (GAN) and fNSDE with a self-attention module. …”
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Exactly solvable diffusions from space-time transformations by Costantino Di Bello, Édgar Roldán, Ralf Metzler

“…We consider a general one-dimensional overdamped diffusion model described by the Itô stochastic differential equation (SDE) ${\mathrm dX_t = \mu(X_t,t)\mathrm dt+\sigma (X_t,t)\mathrm dW_t}$ , where W _t is the standard Wiener process. …”
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Path integral for multiplicative noise: Generalized Fokker-Planck equation  and entropy production rate in stochastic processes with threshold by F. S. Abril-Bermúdez, C. J. Quimbay, J. E. Trinidad-Segovia, M. A. Sánchez-Granero

“…To do so, the Itô diffusive process is generalized by incorporating a multiplicative noise term [η(t)] that affects the diffusive coefficient in the stochastic-differential equation. Then, using the Parisi-Sourlas method, we estimate the transition probability between states of a stochastic variable [X(t)] based on the cumulant-generating function (K_{η}) of the noise. …”
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Unreliable communication in high-performance distributed multi-agent systems: A ingenious scheme in high computing by Ali Mustafa, Muhammad Najam ul Islam, Salman Ahmed, Muhammad Ahsan Tufail

“…The proposed algorithm paces up the rate of convergence by reducing the number of iteration, along with sure convergence of the designed algorithm using the concepts of stochastic differential equation theory, control system theory, algebraic graph theory, and algebraic matrix theory. …”
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Modeling and Analysis of Mixed Traffic Flow Considering Driver Stochasticity and CAV Connectivity Uncertainty by Qi Zeng, Siyuan Hao, Nale Zhao, Ruiche Liu

“…The proposed framework can capture the inherent stochastic variations in human driving behavior by extending the classic intelligent driver model (IDM) with a Langevin-type stochastic differential equation. A car-following model with multi-anticipation control is developed for CAVs, explicitly incorporating sensor noise, communication delays, and dynamic connectivity. …”
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Single-cell multi-omics-based immune temporal network resolution in sepsis: unravelling molecular mechanisms and precise therapeutic targets by Han Liu, Qun Liang

“…Ordinary and stochastic differential-equation models quantified pro-/anti-inflammatory flux.ResultsMulti-omics fusion increased immune-cell classification accuracy from 72.3% to 89.4% (adjusted Rand index, p&lt; 0.001). …”
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Electron Acceleration at Shock Ripples: Role of Pitch-angle Diffusion by Y. D. Xu, G. Li, S. Yao

“…A Monte Carlo simulation on the equivalent time-forward Itô stochastic differential equation is performed within a periodic box to obtain the phase-space distribution function of the accelerated electrons. …”
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Real-world defocus deblurring via score-based diffusion models by Yuhao Li, Haoran Fang, Xiang Lei, Qi Wang, Gang Hu, Jiaqing Dong, Zilong Li, Jiabin Lin, Qiegen Liu, Xianlin Song

“…The method trains a score network by learning the score function of focused images at different noise levels and reconstructs high-quality images through reverse-time stochastic differential equation (SDE). A prediction-correction (PC) framework corrects discretization errors in the reverse-time SDE to enhance the robustness of images during reconstruction. …”
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A Stochastic Model for Adsorption Kinetics by Silvia Rodríguez-Narciso, Juan Antonio Lozano-Álvarez, Rogelio Salinas-Gutiérrez, Netzahualcóyotl Castañeda-Leyva

“…The developed model is the first to describe pollutant removal kinetics based on a stochastic differential equation.…”
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Two-Stage Locating and Capacity Optimization Model for the Ultra-High-Voltage DC Receiving End Considering Carbon Emission Trading and Renewable Energy Time-Series Output Reconstru... by Lang Zhao, Zhidong Wang, Hao Sheng, Yizheng Li, Tianqi Zhang, Yao Wang, Haifeng Yu

“…In this paper, we first start with the description and analysis of the uncertainty in renewable energy (RE) sources, such as wind and solar, and reconstruct the time-sequence power model by using the stochastic differential equation model. Then, a carbon emission trading cost (CET) model is constructed based on the CET mechanism, and the two-stage locating and capacity optimization model for the UHV DC receiving end is proposed under the constraint of dispatch safety and stability. …”
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Bridge, Reverse Bridge, and Their Control by Andrea Baldassarri, Andrea Puglisi

“…To address this question, we compare the stochastic differential equation describing the bridge, derived equivalently via Doob’s transform or stochastic optimal control, with the corresponding equation for the time-reversed bridge. …”
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