Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userAveraging principle for slow-fast stochastic partial differential equations with H{o}lder continuous coefficients
183
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
By using the technique of the Zvonkins transformation and the classical Khasminkiis time discretization method, we prove the averaging principle for slow-fast stochastic partial differential equations with bounded and H{o}lder continuous drift coefficients. An example is also provided to explain our result.
rate research
Read More
This paper is devoted to proving the strong averaging principle for slow-fast stochastic partial differential equations with locally monotone coefficients, where the slow component is a stochastic partial differential equations with locally monotone coefficients and the fast component is a stochastic partial differential equations (SPDEs) with strongly monotone coefficients. The result is applicable to a large class of examples, such as the stochastic porous medium equation, the stochastic $p$-Laplace equation, the stochastic Burgers type equation and the stochastic 2D Navier-Stokes equation, which are the nonlinear stochastic partial differential equations. The main techniques are based on time discretization and the variational approach to SPDEs.
A large deviation principle is derived for stochastic partial differential equations with slow-fast components. The result shows that the rate function is exactly that of the averaged equation plus the fluctuating deviation which is a stochastic partial differential equation with small Gaussian perturbation. This also confirms the effectiveness of the approximation of the averaged equation plus the fluctuating deviation to the slow-fast stochastic partial differential equations.
This work is devoted to averaging principle of a two-time-scale stochastic partial differential equation on a bounded interval $[0, l]$, where both the fast and slow components are directly perturbed by additive noises. Under some regular conditions on drift coefficients, it is proved that the rate of weak convergence for the slow variable to the averaged dynamics is of order $1-varepsilon$ for arbitrarily small $varepsilon>0$. The proof is based on an asymptotic expansion of solutions to Kolmogorov equations associated with the multiple-time-scale system.
This paper is concerned with solution in H{o}lder spaces of the Cauchy problem for linear and semi-linear backward stochastic partial differential equations (BSPDEs) of super-parabolic type. The pair of unknown variables are viewed as deterministic spatial functionals which take values in Banach spaces of random (vector) processes. We define suitable functional H{o}lder spaces for them and give some inequalities among these H{o}lder norms. The existence, uniqueness as well as the regularity of solutions are proved for BSPDEs, which contain new assertions even on deterministic PDEs.
It is well-known that for a one dimensional stochastic differential equation driven by Brownian noise, with coefficient functions satisfying the assumptions of the Yamada-Watanabe theorem cite{yamada1,yamada2} and the Feller test for explosions cite{feller51,feller54}, there exists a unique stationary distribution with respect to the Markov semigroup of transition probabilities. We consider systems on a restricted domain $D$ of the phase space $mathbb{R}$ and study the rate of convergence to the stationary distribution. Using a geometrical approach that uses the so called {it free energy function} on the density function space, we prove that the density functions, which are solutions of the Fokker-Planck equation, converge to the stationary density function exponentially under the Kullback-Leibler {divergence}, thus also in the total variation norm. The results show that there is a relation between the Bakry-Emery curvature dimension condition and the dissipativity condition of the transformed system under the Fisher-Lamperti transformation. Several applications are discussed, including the Cox-Ingersoll-Ross model and the Ait-Sahalia model in finance and the Wright-Fisher model in population genetics.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
