The signature of a rough path: uniqueness by Geng, X

“…As an independent interest, we also develop the Euler-Maruyama scheme for stochastic differential equations driven by <em>G</em>-Brownian motion.…”

Stochastic gradient descent with random label noises: doubly stochastic models and inference stabilizer by Haoyi Xiong, Xuhong Li, Boyang Yu, Dongrui Wu, Zhanxing Zhu, Dejing Dou

“…Specifically, we analyze the learning dynamics of SGD over the quadratic loss with unbiased label noise (ULN), where we model the dynamics of SGD as a stochastic differentiable equation with two diffusion terms (namely a doubly stochastic model). …”
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How to perform the coherent measurement of a curved phase space by continuous isotropic measurement. I. Spin and the Kraus-operator geometry of $\mathrm{SL}(2,\mathbb{C})$ by Christopher S. Jackson, Carlton M. Caves

“…Three equivalent stochastic techniques, (Wiener) path integral, (Fokker-Planck) diffusion equation, and stochastic differential equations, are applied to show that the continuous isotropic POVM quickly limits to the SCS POVM, placing spherical phase space at the boundary of the fundamental Lie group $\mathrm{SL}(2,{\mathbb C})$ in an operationally meaningful way. …”
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Simulation estimation of continuous-time models with applications to finance by Elerian, O

“…Finance in particular has drawn upon and developed the theory of stochastic differential equations. These produce elegant and tractable frameworks which help us to better understand the world. …”

Uncertain execution in order-driven markets by Sanchez Betancourt, L

“…The price limit of each MLO is characterized as the solution to a new class of forward-backward stochastic differential equations (FBSDEs) driven by random measures. …”

Stochastic optimisation model of oil refinery industry and uncertainty quantification in scenario tree of pricing and demand by Mohd. Noh, Norshela

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Application of software engineering methodologies to the development of mathematical biological models by Gill, MS

“…We introduce stochastic constructs to the <em>Ode</em> DSL that enable models to use Stochastic Differential Equations (SDEs), the Stochastic Simulation Algorithm (SSA), and hybrid methods. …”

Discrete approximations in stochastic rough path theory by Flint, G

“…<p>We consider two discrete schemes for studying and approximating stochastic differential equations (SDEs) using the theory of rough paths.…”

Stochastic optimisation model of oil refinery industry and uncertainty quantification in scenario tree of pricing and demand by Mohd. Noh, Norshela

“…In this study, oil prices are modelled and forecasted based on the hurst value, and stochastic differential equations are explored to analyse the uncertainty of the time series. …”
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Stochastic model of cancer growth with the effect of glycosaminoglycans (GAGs) as anticancer therapeutics by Mazma Syahidatul Ayuni, Mazlan

“…Ordinary differential equations (ODEs) and stochastic differential equations (SDEs) have been widely used to describe the biological process of cancer growth. …”
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Mathematical Techniques of Fractional Order Systems / by Azar, Ahmad Taher, editor 629881, Radwan, Ahmed G., editor 648514, Vaidyanathan, Sundarapandian, editor 648515, ScienceDirect (Online service) 7722

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Volatilidad en Opciones Reales: Revisión Literaria y un Caso de Aplicación en el Sector Petrolero Colombiano || Real Options Volatility: Literature Review and a Case of Application... by Pareja Vasseur, Julián. DBA, Prada Sánchez, Marcela, Moreno Escobar, Martha

“…It is proposed that for future research, unbiasedness condition is maintained, but that the estimate is conditional through econometric models, in order to emulate the irregularities and empirical characteristics presented in the financial series using, for example, an appropriate system of stochastic differential equations, as required condition for the performance of price, and the volatility of the underlying asset.…”
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Stochastic modelling of cancer cell proliferation and death in response to anticancer therapeutics of thymoquinone by Shabana, Tabassum

“…This research is aimed to formulate a system of stochastic differential equations (SDEs) for the apoptosis process in signalling pathways of cancer cell proliferation and death in response to TQ. …”
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A Divestment Model: Migration to Green Energy Investment Portfolio Concept by Gaoganwe Sophie Moagi, Obonye Doctor, Edward Lungu

“…To guide the growth of the total wealth in this study, we compared it to the Øksendal and Sulem (Backward Stochastic Differential Equations and Risk Measures (2019)) total wealth for which <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mstyle displaystyle="true"><mrow><mi>c</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mn>0</mn><mo>,</mo></mrow></mstyle></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mstyle displaystyle="true"><mrow><mi>π</mi><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mstyle></semantics></math></inline-formula> is a constant. …”
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Dynamically orthogonal field equations for stochastic fluid flows and particle dynamics by Sapsis, Themistoklis P

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Stochastic Dynamically Orthogonal Modeling and Bayesian Learning for Underwater Acoustic Propagation by Hajj Ali, Wael

“…In the first part, we derive, discretize, implement, and verify stochastic differential equations that (i) capture dominant input uncertainties in the environment (e.g., ocean, bathymetry, and seabed) and in the acoustic parameters (e.g. source location, frequency, and bandwidth), and (ii) predict the acoustic pressure fields and their probability distributions, respecting the nonlinear governing equations and non- Gaussian statistics. …”
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Computational modelling of the biological and social factors of type 2 diabetes by Dutta, Pritha

“…The result is a set of stochastic differential equations which capture the temporal dynamics, by assuming that groups of data-points are subject to the same free energy landscape and amount of noise. …”
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