Results 21 to 30 of about 1,033 (70)

A Schauder estimate for stochastic PDEs [PDF]

, 2015
Considering stochastic partial differential equations of parabolic type with random coefficients in vector-valued H\"older spaces, we obtain a sharp Schauder estimate.
Du, Kai, Liu, Jiakun
core   +4 more sources

Optimizing the Fractional Power in a Model with Stochastic PDE Constraints

Advanced Nonlinear Studies, 2018
We study an optimization problem with SPDE constraints, which has the peculiarity that the control parameter s is the s-th power of the diffusion operator in the state equation.
Geldhauser Carina, Valdinoci Enrico
doaj   +1 more source

A dynamical approximation for stochastic partial differential equations [PDF]

, 2007
Random invariant manifolds often provide geometric structures for understanding stochastic dynamics. In this paper, a dynamical approximation estimate is derived for a class of stochastic partial differential equations, by showing that the random ...
Blömker D., Constantin P., Jinqiao Duan, Keller H., Robinson J. C., Wei Wang   +5 more
core   +2 more sources

Stochastic averaging lemmas for kinetic equations [PDF]

, 2012
We develop a class of averaging lemmas for stochastic kinetic equations. The velocity is multiplied by a white noise which produces a remarkable change in time scale.
Lions, Pierre-Louis, Perthame, Benoit, Souganidis, Panagiotis E.   +2 more
core   +4 more sources

A comparison theorem for backward SPDEs with jumps

, 2014
In this paper we obtain a comparison theorem for backward stochastic partial differential equation (SPDEs) with jumps. We apply it to introduce space-dependent convex risk measures as a model for risk in large systems of interacting ...
Sulem, Agnès, Zhang, Tusheng, Øksendal, Bernt   +2 more
core   +2 more sources

Non-Existence of Positive Stationary Solutions for a Class of Semi-Linear PDEs with Random Coefficients [PDF]

, 2010
We consider a so-called random obstacle model for the motion of a hypersurface through a field of random obstacles, driven by a constant driving field. The resulting semi-linear parabolic PDE with random coefficients does not admit a global nonnegative ...
G. R. Grimmett, J. Xin, L. A. Caffarelli, L. Nirenberg, N. Dirr, N. Dirr, P.-L. Lions, S. Brazovsii   +7 more
core   +3 more sources

Solution theory of fractional SDEs in complete subcritical regimes

Forum of Mathematics, Sigma
We consider stochastic differential equations (SDEs) driven by a fractional Brownian motion with a drift coefficient that is allowed to be arbitrarily close to criticality in a scaling sense.
Lucio Galeati, Máté Gerencsér
doaj   +1 more source

Linear-implicit strong schemes for Itô-Galkerin approximations of stochastic PDEs [PDF]

, 2010
Linear-implicit versions of strong Taylor numerical schemes for finite dimensional Itô stochastic differential equations (SDEs) are shown to have the same order as the original scheme.
Kloeden, Peter E., Shott, Stephen
core  

Well-posedness of the stochastic transport equation with unbounded drift

, 2017
The Cauchy problem for a multidimensional linear transport equation with unbounded drift is investigated. Provided the drift is Holder continuous , existence, uniqueness and strong stability of solutions are obtained.
Mollinedo, David A. C., Olivera, Christian   +1 more
core   +1 more source

An invariant in shock clustering and Burgers turbulence

, 2012
1-D scalar conservation laws with convex flux and Markov initial data are now known to yield a completely integrable Hamiltonian system. In this article, we rederive the analogue of Loitsiansky's invariant in hydrodynamic turbulence from the perspective ...
Burgers J M, Burgers J M, Burgers J M, Burgers J M, Burgers J M, Carraro L, Kolmogorov A N, Loitsianskii L G, Menon G, Ravi Srinivasan, Woyczyński W A   +10 more
core   +1 more source