A higher-order numerical framework for stochastic simulation of chemical reaction systems by Szekely, 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.…”

Numerical methods for foreign exchange option pricing under hybrid stochastic and local volatility models by Cozma, A

“…We analyze exponential integrability properties of Euler discretizations for the square-root process driving the stochastic volatility and the short rates, properties which play a key role in establishing the finiteness of moments and the strong convergence of numerical approximations for a large class of stochastic differential equations in finance, including the ones studied in this thesis. …”

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. …”

Performance of 5-stage, 4-stage and specific stochastic Runge-Kutta methods in approximating the solution of stochastic biological model by Noor Amalina Nisa, Ariffin, Norhayati, Rosli, Abdul Rahman, Mohd Kasim, Mazma Syahidatul Ayuni, Mazlan

“…In recent years, the transition on modelling physical systems via stochastic differential equations (SDEs) has attracted great interest among researchers. …”
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Artificial Intelligence and Mathematical Models of Power Grids Driven by Renewable Energy Sources: A Survey by Sabarathinam Srinivasan, Suresh Kumarasamy, Zacharias E. Andreadakis, Pedro G. Lind

“…These models can be classified as AI- or mathematically inspired models and include dynamical systems, Bayesian inference, stochastic differential equations, machine learning methods, deep learning, reinforcement learning, and reservoir computing. …”
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Precision in disease dynamics: Finite difference solutions for stochastic epidemics with treatment cure and partial immunity by Muhammad Shoaib Arif, Kamaleldin Abodayeh, Yasir Nawaz

“…The scheme can be considered as the extension of the Euler Maruyama scheme for solving stochastic differential equations. The Euler Maruyama scheme offers a first-order accuracy of the deterministic model. …”
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A Probabilistic Physico-Chemical Diffusion Model of the Key Drifting Parameter of Measuring Equipment by Rustam Khayrullin

“…The need for a probabilistic formulation of the problem is argued, since classical statistical methods are not applicable due to the lack of statistical data. (3) Statement of the research problem: A probabilistic formulation of the problem is given taking into account the physical and chemical laws of aging and degradation. (4) Methods: The author uses methods of probability theory and mathematical statistics, methods for solving the stochastic differential equations, the methods of mathematical modeling, the methods of chemical kinetics and the methods for solving a partial differential equations. (5) Results: A mathematical model of a drifting key parameter of measuring equipment is developed. …”
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Simultaneous Measurements of Noncommuting Observables: Positive Transformations and Instrumental Lie Groups by Christopher S. Jackson, Carlton M. Caves

“…This diffusion can be analyzed using Wiener path integration, stochastic differential equations, or a Fokker-Planck-Kolmogorov equation. …”
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Synthetic neuronal datasets for benchmarking directed functional connectivity metrics by João Rodrigues, Alexandre Andrade

“…The generative models covered here are AR processes, neural mass models consisting of linear and nonlinear stochastic differential equations and populations with thousands of spiking units. …”
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Stratifications and foliations in phase portraits of gene network models by V. P. Golubyatnikov, A. A. Akinshin, N. B. Ayupova, L. S. Minushkina

“…Description of the phase portraits of these systems at the level of their stratifications, and that of ensembles of trajectories allows one to construct more realistic gene network models on the basis of methods of statistical physics and the theory of stochastic differential equations.…”
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Theory of spike-train power spectra for multidimensional integrate-and-fire neurons by Sebastian Vellmer, Benjamin Lindner

“…Most popular is a version with Gaussian noise and adaptation currents that can be described via Markovian embedding by a set of d+1 stochastic differential equations corresponding to a Fokker-Planck equation (FPE) for one voltage and d auxiliary variables. …”
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A mixed-effects stochastic model reveals clonal dominance in gene therapy safety studies by Luca Del Core, Danilo Pellin, Ernst C. Wit, Marco A. Grzegorczyk

“…Thus, clonal tracking data can be used to calibrate the stochastic differential equations describing clonal population dynamics and hierarchical relationships in vivo. …”
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Improving representation learning on graph-structural data for classification, generation, and recommendation by Luo, Tianze

“…GSDM utilizes low-rank diffusion Stochastic Differential Equations in graph spectrum space, enhancing graph topology generation and reducing computational load. …”
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Contributions to the numerics of quadratic backward SDEs and probability on turbulence by Zhou, M

“…<p>In this thesis, we first study the numerical scheme of path-dependent quadratic backward stochastic differential equations (quadratic BSDE or QBSDE for short). …”

The computation of Greeks with multilevel Monte Carlo by Burgos, S

“…</p> <p>We present several important results on the moments of the solutions of stochastic differential equations and their discretisations as well as the principles of the so-called “extreme path analysis”. …”

An Edgeworth Expansion for the Ratio of Two Functionals of Gaussian Fields and Optimal Berry–Esseen Bounds by Yoon-Tae Kim, Hyun-Suk Park

“…This form very frequently appears in the estimation problem of parameters occurring in Stochastic Differential Equations (SDEs) and Stochastic Partial Differential Equations (SPDEs). …”
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Efficient Sampling Methods of, by, and for Stochastic Dynamical Systems by Zhang, Benjamin Jiahong

“…This thesis presents new methodologies that lie at the intersection of computational statistics and computational dynamics. Stochastic differential equations (SDEs) are used to model a variety of physical systems, and computing expectations over marginal distributions of SDEs is important for the analysis of such systems. …”
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Sequence-to-sequence learning for motion prediction and generation by Wu, Shuang

“…Finally, we reconsider motion prediction within the framework of stochastic differential equations, which allows for interpretation of model weights as the stochastic diffusion matrix and drift parameters. …”
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Mathematical modelling approaches to understanding the spread of Campylobacter in broiler flocks by Rawson, TE

“…Firstly, I present a mechanistic model system of stochastic differential equations to demonstrate the population dynamics of multiple strains of Campylobacter at both in-host and flock level. …”

Stochastic models of ion channel dynamics and their role in short-term repolarisation variability in cardiac cells by Dangerfield, CE

“…Two different models of stochastic ion channel behaviour, both based on a system of stochastic differential equations (SDEs), are developed and compared. …”