Results 11 to 20 of about 973 (54)
Generalized random processes and Cauchy′s problem for some partial differential systems
International Journal of Mathematics and Mathematical Sciences, Volume 3, Issue 3, Page 549-558, 1980., 1979 In this paper we consider a parabolic partial differential system of the form DtHt = L(t, x, D)Ht. The generalized stochastic solutions Ht, corresponding to the generalized stochastic initial conditions H0 are given. Some properties concerning these generalized stochastic solutions are also obtained.
Mahmoud M. El-Borai
wiley +1 more source
HIGH ORDER PARACONTROLLED CALCULUS
Forum of Mathematics, Sigma, 2019 We develop in this work a general version of paracontrolled calculus that allows to treat analytically within this paradigm a whole class of singular partial differential equations with the same efficiency as regularity structures.
ISMAËL BAILLEUL, FRÉDÉRIC BERNICOT
doaj +1 more source
Quasilinear parabolic stochastic partial differential equations: existence, uniqueness [PDF]
, 2015 In this paper, we provide a direct approach to the existence and uniqueness of strong (in the probabilistic sense) and weak (in the PDE sense) solutions to quasilinear stochastic partial differential equations, which are neither monotone nor locally ...
Hofmanova, Martina, Zhang, Tusheng
core +3 more sources
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. +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 +2 more
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 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 +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 +7 more
core +3 more sources
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
Solution theory of fractional SDEs in complete subcritical regimes
Forum of Mathematics, SigmaWe 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