Numerical Solution Of Sde Through Computer Experiments

By Sarah Rothstein. 2016

234 citations recorded by the source corpus.

Subfields: Finance

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Flow Matching for Generative Modeling (2022, neutral): “In part, this is due to ODE solvers being much more efficient—yielding lower error at similar computational costs (Kloeden et al., 2012)—and the multitude of available ODE solver schemes.”
Matching Normalizing Flows and Probability Paths on Manifolds (2022, methodology): “In fact, below we construct paths for which an SDE/PDE characterization is not known.”
Loss of regularity for Kolmogorov equations (2012, background): “, the books and overview articles [42, 43, 52, 24, 3, 53, 56, 38, 41] for extensive lists of references.”
Itô-Taylor Sampling Scheme for Denoising Diffusion Probabilistic Models using Ideal Derivatives (2021, methodology): “One of the simplest numerical schemes for SDEs is the Euler-Maruyama method (Maruyama, 1955, Theorem.”
Environmental variability and mean-reverting processes (2016, background): “Specifically, letting ti+1 − ti = h = 1, integrating equation (39) over [ti, ti+1], and approximating the integral on the right-hand side leads to the Euler-Maruyama approximation [14, 15]: Gi+1 = Gi + ha(Ge −Gi) + b √ h ηi (41) where ηi are normally distributed numbers with zero mean and unit varia”
Comparative Analysis of the Efficiency of Application of Legendre Polynomials and Trigonometric Functions to the Numerical Integration of Ito Stochastic Differential Equations (2018, unknown): “This idea has been developed in [22] - [24].”