-estimates for SPDE with discontinuous coefficients in domains.
-uniqueness for infinite dimensional symmetric Kolmogorov operators : the case of variable diffusion coefficients
Large deviation principle and inviscid shell models.
Large deviation principle for a stochastic heat equation with spatially correlated noise.
Large deviations and support results for nonlinear Schrödinger equations with additive noise and applications
Sample path large deviations for the laws of the solutions of stochastic nonlinear Schrödinger equations when the noise converges to zero are presented. The noise is a complex additive gaussian noise. It is white in time and colored in space. The solutions may be global or blow-up in finite time, the two cases are distinguished. The results are stated in trajectory spaces endowed with topologies analogue to projective limit topologies. In this setting, the support of the law of the solution is also...
Large deviations and support results for nonlinear Schrödinger equations with additive noise and applications
Sample path large deviations for the laws of the solutions of stochastic nonlinear Schrödinger equations when the noise converges to zero are presented. The noise is a complex additive Gaussian noise. It is white in time and colored in space. The solutions may be global or blow-up in finite time, the two cases are distinguished. The results are stated in trajectory spaces endowed with topologies analogue to projective limit topologies. In this setting, the support of the law of the solution is...
Large deviations for invariant measures of stochastic reaction–diffusion systems with multiplicative noise and non-Lipschitz reaction term
Law equivalence of solutions of some linear stochastic equations in Hilbert spaces
Sufficient and necessary conditions for equivalence of the distributions of the solutions of some linear stochastic equations in Hilbert spaces are given. Some facts in the theory of perturbations of semigroup generators and Zabczyk's results on law equivalence are used.
Linear stochastic parabolic equations, degenerating on the boundary of a domain.
Linear-implicit strong schemes for Itô-Galerkin approximations of stochastic PDEs.
Local Collapses in the Truscott-Brindley Model
Relaxation oscillations are limit cycles with two clearly different time scales. In this article the spatio-temporal dynamics of a standard prey-predator system in the parameter region of relaxation oscillation is investigated. Both prey and predator population are distributed irregularly at a relatively high average level between a maximal and a minimal value. However, the slowly developing complex pattern exhibits a feature of “inverse excitability”: Both populations show collapses which occur...
Local extinction for superprocesses in random environments.
Local solutions for stochastic Navier Stokes equations
Local Solutions for Stochastic Navier Stokes Equations
In this article we consider local solutions for stochastic Navier Stokes equations, based on the approach of Von Wahl, for the deterministic case. We present several approaches of the concept, depending on the smoothness available. When smoothness is available, we can in someway reduce the stochastic equation to a deterministic one with a random parameter. In the general case, we mimic the concept of local solution for stochastic differential equations.
Long-term behavior for superprocesses over a stochastic flow.
Long-time behavior of solutions to a class of quasilinear parabolic equations with random coefficients
Lp-theory for the stochastic heat equation with infinite-dimensional fractional noise
In this article, we consider the stochastic heat equation , with random coefficientsf and gk, driven by a sequence (βk)k of i.i.d. fractional Brownian motions of index H>1/2. Using the Malliavin calculus techniques and a p-th moment maximal inequality for the infinite sum of Skorohod integrals with respect to (βk)k, we prove that the equation has a unique solution (in a Banach space of summability exponent p ≥ 2), and this solution is Hölder continuous in both time and space.
Lp-theory for the stochastic heat equation with infinite-dimensional fractional noise*
In this article, we consider the stochastic heat equation , with random coefficients f and gk, driven by a sequence (βk)k of i.i.d. fractional Brownian motions of index H>1/2. Using the Malliavin calculus techniques and a p-th moment maximal inequality for the infinite sum of Skorohod integrals with respect to (βk)k, we prove that the equation has a unique solution (in a Banach space of summability exponent p ≥ 2), and this solution is Hölder continuous in both time and space.
Lyapunov exponents for the parabolic Anderson model.