Rate of Convergence of Space Time Approximations for Stochastic Evolution Equations
By István Gyöngy, Annie Millet. 2007
104 citations recorded by the source corpus.
Stochastic evolution equations in Banach spaces with unbounded nonlinear drift and diffusion operators driven by a finite dimensional Brownian motion are considered. Under some regularity condition assumed for the solution, the rates of convergence of various numerical approximations are estimated under strong monotonicity and Lipschitz conditions. The abstract setting involves general consistency conditions and is then applied to a class of quasilinear stochastic PDEs of parabolic type.
Subfields: Applied Mathematics, Finance, Management Science and Operations Research
View Paper: https://www.semanticscholar.org/paper/f6b34531cdfa2602eafb3c9807432c81fc6b04d3
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Wei Liu
- Tusheng Zhang
- Michael Röckner
- Shijie Shang
- Xicheng Zhang
- Feng-Yu Wang
- Giuseppe Da Prato
- Franco Flandoli
In Finance
- Tusheng Zhang
- Wei Liu
- Michael Röckner
- Shijie Shang
- Xicheng Zhang
- Feng-Yu Wang
- A. Budhiraja
- Paul Dupuis
In Management Science and Operations Research
Citations in the corpus
- SPDE in Hilbert space with locally monotone coefficients (2010, methodology): “see [8, 19, 28, 32] for the small noise large deviation principle, [13, 14] for discretization approximation schemes to the solutions of SPDE, [34, 17, 18] for the dimension-free Harnack inequality and resulting ergodicity, compactness and contractivity properties of the associated transition semigr”
- 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”
- Random attractors for a class of stochastic partial differential equations driven by general additive noise (2010, unknown): “see (H1) − (H4) in [24, 25, 34, 35, 36, 42] and (H2) in [19, 34, 36].”