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We study the hyperbolic $\Phi^{k+ 1} _2 $-model on the plane. By establishing coming down
from infinity for the associated stochastic nonlinear heat equation (SNLH) on the plane, we …

This article is concerned with the almost sure existence of global solutions for initial value
problems of the form γ˙(t)= v (t, γ (t)) on separable dual Banach spaces. We prove a general …

We show probabilistic existence and uniqueness for the Wick-ordered cubic nonlinear wave
equation in a weighted Besov space over $\mathbb R^ 2$. To achieve this, we show that a …

In this paper, we consider a certain class of second order nonlinear PDEs with damping and
space-time white noise forcing, posed on the d-dimensional torus. This class includes the …

We construct dynamics for the defocusing real-valued (Miura) mKdV equation on the real
line with initial data distributed according to Gibbs measure. We also prove that Gibbs …

In this paper, we are concerned with the study of statistical equilibria for focusing nonlinear
Schr\" odinger and Hartree equations on the d-dimensional torus when d= 1, 2, 3. Due to the …

This thesis consists of two parts. Part I studies a special class of oscillating nonlinear
differential equations in finite dimensional spaces. Under integrability conditions, a «blow …