Approximate Integration of Stochastic Differential Equations

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Previous article Next article Approximate Integration of Stochastic Differential EquationsG. N. Mil’shtejnG. N. Mil’shtejnhttps://doi.org/10.1137/1119062PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] I. I. Gikhman and , A. V. Skorokhod, Introduction to the Theory of Random Processes, Izd-vo “Nauka”, Moscow, 1965, (In Russian.) Google Scholar[2] I. I. Gikhman and , A. V. Skorokhod, Stochastic Differential Equations, Springer, New York, 1972 0242.60003 CrossrefGoogle Scholar[3] R. Z. Khas'minskii, Stability of Systems of Differential Equations under Random Perturbations of their Parameters, Izd-vo “Nauka”, Moscow, 1969, (In Russian.) Google Scholar[4] E. Hills and , R. Phillips, Functional Analysis and Semigroups, American Mathematical Society, Providence, RI., 1957 0078.10004 Google Scholar[5] R. L. Stratonovich, Conditional Markov processes and their application to the theory of optimal control, Translated from the Russian by R. N. and N. B. McDonough for Scripta Technica, Inc. Modern Analytic and Computational Methods in Science and Mathematics, No. 7, American Elsevier Publishing Co., Inc., New York, 1968xvii+350 MR0221860 (36:4912) 0159.46804 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Simulating systems of Itô SDEs with split-step $ (\alpha, \beta) $-Milstein schemeAIMS Mathematics, Vol. 8, No. 2 Cross Ref Impact of flow field resolution on produced water transport in Lagrangian and Eulerian modelsMarine Pollution Bulletin, Vol. 182 Cross Ref Manifold Markov chain Monte Carlo methods for Bayesian inference in diffusion models19 April 2022 | Journal of the Royal Statistical Society: Series B (Statistical Methodology), Vol. 84, No. 4 Cross Ref Monte Carlo Simulation of Stochastic Differential Equation to Study Information Geometry12 August 2022 | Entropy, Vol. 24, No. 8 Cross Ref Planktos: An Agent-Based Modeling Framework for Small Organism Movement and Dispersal in a Fluid Environment with Immersed Structures10 June 2022 | Bulletin of Mathematical Biology, Vol. 84, No. 7 Cross Ref Pricing path-dependent exotic options with flow-based generative networksApplied Soft Computing, Vol. 124 Cross Ref Estimation of drift and diffusion functions from unevenly sampled time-series data27 July 2022 | Physical Review E, Vol. 106, No. 1 Cross Ref The Generalized Gamma Distribution as a Useful RND under Heston’s Stochastic Volatility Model26 May 2022 | Journal of Risk and Financial Management, Vol. 15, No. 6 Cross Ref On the approximation and simulation of iterated stochastic integrals and the corresponding Lévy areas in terms of a multidimensional Brownian motion26 May 2021 | Stochastic Analysis and Applications, Vol. 40, No. 3 Cross Ref Brownian particles driven by spatially periodic noise1 March 2022 | The European Physical Journal E, Vol. 45, No. 3 Cross Ref The Seven-League Scheme: Deep Learning for Large Time Step Monte Carlo Simulations of Stochastic Differential Equations23 February 2022 | Risks, Vol. 10, No. 3 Cross Ref 1 January 2022 Cross Ref Learning Stochastic Optimal Policies via Gradient DescentIEEE Control Systems Letters, Vol. 6 Cross Ref A Closed Form Solution for Pricing Variance Swaps Under the Rescaled Double Heston Model27 November 2021 | Computational Economics, Vol. 11 Cross Ref Cell-cell communication through FGF4 generates and maintains robust proportions of differentiated cell types in embryonic stem cells5 November 2021 | Development, Vol. 148, No. 21 Cross Ref On Multilevel and Control Variate Monte Carlo Methods for Option Pricing under the Rough Heston Model17 November 2021 | Mathematics, Vol. 9, No. 22 Cross Ref Mathematical modelling of the second wave of COVID-19 infections using deterministic and stochastic SIDR models7 July 2021 | Nonlinear Dynamics, Vol. 106, No. 2 Cross Ref A Local and Time Resolution of the COVID-19 Propagation—A Two-Dimensional Approach for Germany Including Diffusion Phenomena to Describe the Spatial Spread of the COVID-19 Pandemic7 July 2021 | Physics, Vol. 3, No. 3 Cross Ref Deep learning-based least squares forward-backward stochastic differential equation solver for high-dimensional derivative pricing26 March 2021 | Quantitative Finance, Vol. 21, No. 8 Cross Ref Information Transmission in Delay-Coupled Neuronal Circuits in the Presence of a Relay Population29 July 2021 | Frontiers in Systems Neuroscience, Vol. 15 Cross Ref Efficient simulation methods for the Quasi-Gaussian term-structure model with volatility smiles: practical applications of the KLNV-scheme4 February 2021 | Quantitative Finance, Vol. 21, No. 7 Cross Ref Convergence, non-negativity and stability of a new Lobatto IIIC-Milstein method for a pricing option approach based on stochastic volatility model18 September 2020 | Japan Journal of Industrial and Applied Mathematics, Vol. 38, No. 2 Cross Ref Active noise-driven particles under space-dependent friction in one dimension4 May 2021 | Physical Review E, Vol. 103, No. 5 Cross Ref Transmission delays and frequency detuning can regulate information flow between brain regions15 April 2021 | PLOS Computational Biology, Vol. 17, No. 4 Cross Ref On the MS-stability of predictor–corrector schemes for stochastic differential equationsMathematics and Computers in Simulation, Vol. 180 Cross Ref Deep Splitting Method for Parabolic PDEsChristian Beck, Sebastian Becker, Patrick Cheridito, Arnulf Jentzen, and Ariel Neufeld13 September 2021 | SIAM Journal on Scientific Computing, Vol. 43, No. 5AbstractPDF (580 KB)A Kinetic Monte Carlo Approach for Simulating Cascading Transmission Line FailureJacob Roth, David A. 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