A Concise Course on Stochastic Partial Differential Equations

By Claudia Prévôt, Michael Röckner. 2007

1,136 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Finance, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/93c030b83bfefb23546f1c71e4fc2ade0911f656

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

1. Michael Röckner
2. Wei Liu
3. Xicheng Zhang
4. Feng-Yu Wang
5. Franco Flandoli
6. Tusheng Zhang
7. Longjie Xie
8. Giuseppe Da Prato

In Finance

1. Michael Röckner
2. Wei Liu
3. Xicheng Zhang
4. Feng-Yu Wang
5. Tusheng Zhang
6. Benjamin Gess
7. Giuseppe Da Prato
8. Franco Flandoli

In Numerical Analysis

1. Wei Liu
2. Claude Jeffrey Gittelson
3. Arnulf Jentzen
4. Feng-Yu Wang
5. Enrico Priola
6. Longjie Xie
7. Michael Röckner
8. Giuseppe Da Prato

Citations in the corpus

• Parameter estimation for the stochastically perturbed Navier-Stokes equations (2010, methodology): “We briefly recall the classical formalism for infinite-dimensional Wiener process as in [8], [34].”
• Well-posedness of stochastic partial differential equations with Lyapunov condition (2013, background): “Moreover, we should remark that the main result is also applicable to stochastic fast diffusion equations, stochastic Burgers type equations and stochastic reaction–diffusion equations having any (odd) degree polynomial perturbation with negative leading coefficient in the drift, which avoid the sta”
• Stochastic Variational Inequalities and Applications to the Total Variation Flow Perturbed by Linear Multiplicative Noise (2012, background): “11) Then, by the standard existence theory for stochastic differential equations associated with nonlinear monotone and demicontinuous operators in a duality pair (V, V ) ([27], [29], [30]) equation (5.”
• An operatorial approach to stochastic partial differential equations driven by linear multiplicative noise (2014, neutral): “8(iii) of [16], respectively, can be applied due to Lemma 8.”
• Local and global well-posedness of SPDE with generalized coercivity conditions☆ (2012, methodology): “[39, 50]), which implies continuity in the finite dimensional case.”
• Stochastic non-isotropic degenerate parabolic–hyperbolic equations (2016, background): “[40] C. Prévôt and M. Röckner.”
• A free stochastic partial differential equation (2010, background): “Let us describe first the variational approach, originating from [23,30,31] (we refer to [35], and the recent introductory [34] in the coercive case).”
• Harnack inequality and applications for stochastic evolution equations with monotone drifts (2008, methodology): “AMS Subject Classification: 60H15; 60J35; 47D07.”
• Martingale solutions and Markov selections for stochastic partial differential equations (2009, neutral): “in [9,6,15,3,4,18, 16] (see also [14]).”