22 research outputs found
Optimal Strong Rates of Convergence for a Space-Time Discretization of the Stochastic Allen-Cahn Equation with multiplicative noise
The stochastic Allen-Cahn equation with multiplicative noise involves the
nonlinear drift operator . We use the fact that
satisfies a weak monotonicity property to deduce uniform bounds in strong norms
for solutions of the temporal, as well as of the spatio-temporal discretization
of the problem. This weak monotonicity property then allows for the estimate for all
small , where is the strong variational solution of the
stochastic Allen-Cahn equation, while solves a
structure preserving finite element based space-time discretization of the
problem on a temporal mesh of size which
covers
Stochastic doubly nonlinear PDE: Large Deviation Principles and existence of Invariant measure
In this paper, we establish large deviation principle for the strong solution
of a doubly nonlinear PDE driven by small multiplicative Brownian noise.
Motononicity arguments and the weak convergence approach have been exploited in
the proof. Moreover, by using certain a-priori estimates and sequentially
weakly Feller property of the associated Markov semigroup, we show existence of
invariant probability measure for the strong solution of the underlying
problem.Comment: arXiv admin note: text overlap with arXiv:2210.1103
Continuous dependence estimate for a degenerate parabolic-hyperbolic equation with Levy noise
In this article, we are concerned with a multidimensional degenerate
parabolic-hyperbolic equation driven by Levy processes. Using bounded variation
(BV) estimates for vanishing viscosity approximations, we derive an explicit
continuous dependence estimate on the nonlinearities of the entropy solutions
under the assumption that Levy noise depends only on the solution. This result
is used to show the error estimate for the stochastic vanishing viscosity
method. In addition, we establish fractional BV estimate for vanishing
viscosity approximations in case the noise coefficients depend on both the
solution and spatial variable.Comment: 31 Pages. arXiv admin note: text overlap with arXiv:1502.0249