On Discretization Schemes for Stochastic Evolution Equations

By István Gyöngy, Annie Millet. 2005

114 citations recorded by the source corpus.

Abstract Stochastic evolutional equations with monotone operators are considered in Banach spaces. Explicit and implicit numerical schemes are presented. The convergence of the approximations to the solution of the equations is proved.

Subfields: Finance, Mathematical Physics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/7116918d59fc80a49dca813b361e1bdec34d524e

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The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Finance

1. Wei Liu
2. Michael Röckner
3. Tusheng Zhang
4. Xicheng Zhang
5. Shijie Shang
6. Arnulf Jentzen
7. Annie Millet
8. Sotirios Sabanis

In Mathematical Physics

1. Wei Liu
2. Tusheng Zhang
3. Xicheng Zhang
4. Michael Röckner
5. Annie Millet
6. Shijie Shang
7. Arnulf Jentzen
8. David Siska

In Numerical Analysis

1. Wei Liu
2. Arnulf Jentzen
3. David Siska
4. Sotirios Sabanis
5. Tusheng Zhang
6. Xicheng Zhang
7. István Gyöngy
8. Annie Millet

Citations in the corpus

• Large Deviations for Stochastic Evolution Equations with Small Multiplicative Noise (2008, background): “Stochastic evolution equations have been studied intensively in recent years and we refer to [10, 11, 20, 22, 23, 27, 30, 39, 42] for various generalizations and applications.”
• Strong convergence rates for an explicit numerical approximation method for stochastic evolution equations with non-globally Lipschitz continuous nonlinearities (2015, background): “Moreover, strong convergence but with no rate of convergence of an full-discrete drift-implicit Euler method has, e.g., been proven in Theorem 2.10 in Gyöngy & Millet [7] in the case of some SEEs with non-globally Lipschitz continuous nonlinearities; see also, e.g., Theorem 7.1 in Brzeźniak et al.”
• Convergence of tamed Euler schemes for a class of stochastic evolution equations (2014, methodology): “scheme applied to stochastic evolution equations is convergent (when coupled appropriately with the spatial discretization), see, for example, Gyöngy and Millet [6].”
• Harnack inequality and applications for stochastic evolution equations with monotone drifts (2008, background): “For more general results we refer to [ 12 , 27, 38].”
• Freidlin-Wentzell's Large Deviations for Stochastic Evolution Equations (2008, background): “On the other hand, the existence and uniqueness of SPDEs have already been studied in various literatures prior to LDP for SPDEs(cf. [8, 18, 27, 10, 15, 31], etc.).”
• Rate of Convergence of Space Time Approximations for Stochastic Evolution Equations (2007, background): “In [7] it is shown that under these conditions the solutions of various implicit and explicit schemes converge to u.”
• Well-posedness of stochastic partial differential equations with fully local monotone coefficients (2022, background): “see [48, 27, 5] for regularity of solutions, [18, 74, 47, 19, 88, 52, 61, 87, 37, 38] for large deviation principle, [31, 32, 33, 78, 65, 4, 90] for numerical approximation, [84, 46, 85, 86] for the Harnack inequality, gradient estimates, invariant measure and ergodicity, [28, 29] for random attract”