Understanding the Nature of the Long-Range Memory Phenomenon in Socioeconomic Systems by Rytis Kazakevičius, Aleksejus Kononovicius, Bronislovas Kaulakys, Vygintas Gontis

“…Our group has shown that the long-range memory phenomenon can be reproduced using various Markov processes, such as point processes, stochastic differential equations, and agent-based models—reproduced well enough to match other statistical properties of the financial markets, such as return and trading activity distributions and first-passage time distributions. …”
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Formal verification meets stochastic analysis by Cosentino, F

“…The models studied have a countable states space and this can be considered the main obstacle to extend Formal Verification techniques for the computation of likelihoods in the case of Stochastic Differential Equations. However, the most studied properties in Formal Verification have a clear characterization in Mathematics. …”

A higher-order numerical framework for stochastic simulation of chemical reaction systems. by Székely, T, Burrage, K, Erban, R, Zygalakis, K

“…As in the case of ordinary and stochastic differential equations, extrapolation can be repeated to obtain even higher-order approximations. …”

Learning probabilistic representations for inference, training and interpretability by Abbati, G

“…Second, we propose a novel noise model for Gaussian Processes that, in conjunction with state-of-the-art moment matching and adversarial techniques, addresses the problem of parameter inference in systems of stochastic differential equations. Finally, we move our attention to the optimization and sampling algorithms employed for Bayesian inference. …”

Hybrid equity warrants pricing formulation under stochastic dynamics by Roslan, Teh Raihana Nazirah, Ibrahim, Siti Zulaiha, Karim, Sharmila

“…The development of the model involves the derivations of stochastic differential equations that govern the model dynamics. …”
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Coupled Price–Volume Equity Models with Auto-Induced Regime Switching by Manuel L. Esquível, Nadezhda P. Krasii, Pedro P. Mota, Victoria V. Shamraeva

“…The auto-induced regime-switching models referred to may be based on a finite set of stochastic differential equations (SDE)—all defined on the same bounded time interval—and a sequence of interlacing stopping times defined by the hitting threshold times of the trajectories of the solutions of the SDE. …”
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Assessing mechanisms for microbial taxa and community dynamics using process models by Linwei Wu, Yunfeng Yang, Daliang Ning, Qun Gao, Huaqun Yin, Naija Xiao, Benjamin Y. Zhou, Si Chen, Qiang He, Jizhong Zhou

“…Here, we present a novel approach for quantitatively delineating community assembly mechanisms by combining the consumer–resource model with a neutral model in stochastic differential equations. Using time‐series data from anaerobic bioreactors that target microbial 16S rRNA genes, we tested the applicability of three ecological models: the consumer–resource model, the neutral model, and the combined model. …”
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Innovative stochastic finite difference approach for modelling unsteady non-Newtonian mixed convective fluid flow with variable thermal conductivity and mass diffusivity by Muhammad Shoaib Arif, Muhammad Shoaib Arif, Kamaleldin Abodayeh, Yasir Nawaz, Yasir Nawaz

“…A novel stochastic numerical scheme is introduced to solve stochastic differential equations. The development of the scheme is based on two different parts. …”
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Generalized physics-informed learning through language-wide differentiable programming by Rackauckas, C, Edelman, A, Fischer, K, Innes, M, Saba, E, Shah, VB, Tebbutt, W

“…We showcase several examples of physics-informed learning which directly utilizes this extension to existing simulation code: neural surrogate models, machine learning on simulated quantum hardware, and data-driven stochastic dynamical model discovery with neural stochastic differential equations.…”
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Stochastic modelling of time delay for solvent production by Clostridium Acetobutylicum P262 by Tawfiqullah, Ayoubi

“…Ordinary differential equations (ODEs) and stochastic differential equations (SDEs) are widely used to model biological systems in the last decades. …”
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Stochastic Runge-Kutta method for stochastic delay differential equations by Norhayati, Rosli

“…However,the complexity arises due to the presence of both randomness and time delay.The analytical solution of SDDEs is hard to be found.In such a case, a numerical method provides a way to solve the problem.Nevertheless, due to the lacking of numerical methods available for solving.SDDEs,a wide range of researchers among the mathematicians and scientists have not incorporated the important features of the real phenomena,which include randomness and time delay in modeling the system.Hence,this research aims to generalize the convergence proof of numerical methods for SDDEs when the drift and diffusion functions are Taylor expansion and to develop a stochastic Runge—Kutta for solving SDDEs Motivated by the relative paucity of numerical methods accessible in simulating the strong solution of SDDEs,the numerical schemes developed in this research is hoped to bridge the gap between the evolution of numerical methods in ordinary differential equations(ODEs), delay differential equations (DDEs),stochastic differential equations(SDEs)and SDDEs.The extension of numerical methods of SDDEs is far from complete.Rate of convergence of recent numerical methods available in approximating the solution of SDDEs only reached the order of 1.0. …”
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Volterra dendritic stimulus processors and biophysical spike generators with intrinsic noise sources by Aurel A Lazar, Yiyin eZhou

“…Using a stochastic differential equations formalism we show that encoding with a neuron model consisting of a nonlinear DSP cascaded with a BSG with intrinsic noise sources can be treated as generalized sampling with noisy measurements.For single-input multi-output neural circuit models with feedforward, feedback and cross-feedback DSPs cascaded with BSGs we theoretically analyze the effect of noise sources on stimulus decoding. …”
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Long-Term Bifurcation and Stochastic Optimal Control of a Triple-Delayed Ebola Virus Model with Vaccination and Quarantine Strategies by Anwarud Din, Asad Khan, Yassine Sabbar

“…The perturbed model takes the form of a system of stochastic differential equations. Based on some non-standard analytical techniques, we demonstrate two main approach properties: intensity and elimination of Ebola virus. …”
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Exploring Distributions of House Prices and House Price Indices by Jiong Liu, Hamed Farahani, R. A. Serota

“…We use generalized beta (GB) family of functions to fit distributions of HP and HPI since GB naturally arises from the models of economic exchange described by stochastic differential equations. Our main finding is that HP and multi-year HPI exhibit a negative Dragon King (nDK) behavior, wherein power-law distribution tail gives way to an abrupt decay to a finite upper limit value, which is similar to our recent findings for realized volatility of S&P500 index in the US stock market. …”
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Stochastic evolutionary game analysis of food cooperation among countries along the Belt and Road from the perspective of food security by Mao Qinghua, Xu Linyao, Sun Qilong, Guo Mengxin

“…The level of effort of large cereal countries and the incentives of regulatory committees can have a positive impact, but high income in small cereal countries can lead to instability in the strategic choices of other players.DiscussionTaking the countries along the Belt and Road as the research object, Gaussian white noise is introduced to describe the stochastic external environment, discriminate the stability of the game system through stochastic differential equations, and analyze the influencing factors of the dynamic behavioral strategies of the parties in combination with simulation methods. …”
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OPTIMIZATION OF NONLINEAR STOCHASTIC SYSTEMS IN THE SPECTRAL CHARACTERISTICS OF CONTROLS by K. A. Rybakov

“…The author presents the spectral method of determining relatively optimal control in case of incomplete infor- mation about the state vector for multidimensional nonlinear continuous stochastic systems, which are governed by Itô’s stochastic differential equations. The quality criterion is given as the mean of the function determined on the system tracks. …”
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High-order retractions for reduced-order modeling and uncertainty quantification by Charous, Aaron (Aaron Solomon)

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Generative Stochastic Modeling of Strongly Nonlinear Flows with Non-Gaussian Statistics by Arbabi, Hassan, Sapsis, Themistoklis

“…Here, we propose a data-driven framework to model stationary chaotic dynamical systems through nonlinear transformations and a set of decoupled stochastic differential equations (SDEs). Specifically, we use optimal transport to find a transformation from the distribution of time-series data to a multiplicative reference probability measure such as the standard normal distribution. …”
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Deep learning-based numerical methods for partial differential equations by Dou, Yao

“…The objective of this Final Year Project is to study deep learning-based numerical methods, with a focus on the Deep BSDE Solver, that can be applied on stochastic control problems, backward stochastic differential equations (BSDE) and partial differential equations (PDE) in high-dimensional space. …”
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Discrete and continuum approximations for collective cell migration in a scratch assay with cell size dynamics by Matsiaka, O, Penington, C, Baker, R, Simpson, M

“…Our agent-based stochastic model takes the form of a system of Langevin equations that is the system of stochastic differential equations governing the evolution of the population of agents. …”