We discuss and prove validity of the Hubbard-Stratonovich (HS) identities over hyperbolic domains which are used frequently in the studies on disordered systems and random matrices. We also introduce a counterpart of the HS identity arising in disordered systems with ”chiral” symmetry. Apart from this we outline a way of deriving the nonlinear σ-model from the gauge-invariant Wegner k−orbital m...

We discuss and prove validity of the Hubbard-Stratonovich (HS) identities over hyperbolic domains which are used frequently in the studies on disordered systems and random matrices. We also introduce a counterpart of the HS identity arising in disordered systems with ”chiral” symmetry. Apart from this we outline a way of deriving the nonlinear σ-model from the gauge-invariant Wegner k−orbital m...

We prove a representation formula for solutions of Schrödinger equations with potentials multiplied by a temporal real-valued white noise in the Stratonovich sense. Using this formula, we obtain a dispersive estimate which allows us to study the Cauchy problem in L or in the energy space of model equations arising in Bose Einstein condensation [1] or in fiber optics [2]. Our results also give a...

Abstract We study a wave equation in dimension $d\in \{1,2\}$ with multiplicative space-time Gaussian noise. The existence and uniqueness of the Stratonovich solution is obtained under some conditions imposed on strategy to develop Strichartz-type estimates for kernel weighted Besov spaces, by which we can prove well-posedness an associated Young-type equation. Those Strichartz bounds are indep...

We prove several stability estimates, comparing solutions driven by different (bi,σi), both for Itô and Stratonovich SDEs, possibly depending on negative Sobolev norms of the difference b1−b2. then discuss applications these results to McKean–Vlasov criteria strong compactness Wong–Zakai type theorems.

A recent paper of Melbourne & Stuart, A note on diffusion limits of chaotic skew product flows, Nonlinearity 24 (2011) 1361–1367, gives a rigorous proof of convergence of a fast-slow deterministic system to a stochastic differential equation with additive noise. In contrast to other approaches, the assumptions on the fast flow are very mild. In this paper, we extend this result from continuous ...

Abstract. In this paper we present a rigorous asymptotic analysis for stochastic systems with two fast relaxation times. The mathematical model analyzed in this paper consists of a Langevin equation for the particle motion with time-dependent force constructed through an infinite dimensional Gaussian noise process. We study the limit as the particle relaxation time as well as the correlation ti...