Freidlin-Wentzell's Large Deviations for Stochastic Evolution Equations
By Jiagang Ren, Xicheng Zhang. 2008
76 citations recorded by the source corpus.
We prove a Freidlin-Wentzell large deviation principle for general stochastic evolution equations with small perturbation multiplicative noises. In particular, our general result can be used to deal with a large class of quasi linear stochastic partial differential equations, such as stochastic porous medium equations and stochastic reaction diffusion equations with polynomial growth zero order term and $p$-Laplacian second order term.
Subfields: Computational Theory and Mathematics, Finance, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/dea920bd48ebbadd74e48f96f3b319dfd8ee2d5f
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computational Theory and Mathematics
- Xicheng Zhang
- Tusheng Zhang
- Shijie Shang
- Michael Röckner
- Feng-Yu Wang
- Longjie Xie
- Wei Liu
- Franco Flandoli
In Finance
- Tusheng Zhang
- Xicheng Zhang
- Michael Röckner
- Shijie Shang
- Wei Liu
- Feng-Yu Wang
- A. Budhiraja
- Paul Dupuis
In Mathematical Physics
- Tusheng Zhang
- Shijie Shang
- Michael Röckner
- Xicheng Zhang
- Feng-Yu Wang
- Wei Liu
- Vladimir Bogachev
- Jianhai Bao
Citations in the corpus
- Stochastic 2D Hydrodynamical Type Systems: Well Posedness and Large Deviations (2008, unknown): “Let us also point out that due to the bilinear term which arises in hydrodynamical models, the control of any moment of the V � norm for time increments of the solution is not as good as that in [ 31 ].”
- 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”
- Stochastic Volterra Equations in Banach Spaces and Stochastic Partial Differential Equations (2008, methodology): “We also refer to [47, 66] for the application of weak convergence approach in the LDPs of stochastic evolution equations (the case of evolution triple).”