We revisit the problem of well-defining rotation numbers for discrete random dynamical systems on S. We show that, contrasting with deterministic systems, the topological (i.e. based on Poincaré lifts) approach does depend on the choice of lifts (e.g. continuously for nonatomic randomness). Furthermore, the winding orbit rotation number does not agree with the topological rotation number. Exist...

We study existence and uniqueness of a variational solution in terms of stochastic variational inequalities (SVI) to stochastic nonlinear diffusion equations with a highly singular diffusivity term and multiplicative Stratonovich gradient-type noise. We derive a commutator relation for the unbounded noise coefficients in terms of a geometric Killing vector condition. The drift term is given by ...

We present a mass-preserving scheme for the stochastic nonlinear Schrödinger equation with multiplicative noise of Stratonovich type. It is a splitting scheme and we present an explicit formula for solving the sub-step related to the nonlinear part. The scheme is unconditionally stable in the L2 norm. For the linear stochastic Schrödinger equation, we prove that the scheme has a strong converge...

A nonperturbative theory of the electron propagator is developed and used to calculate the one-particle Green’s function and tunneling density of states in strongly correlated electron systems. The method, which is based on a Hubbard–Stratonovich decoupling of the electron–electron interaction combined with a cumulant expansion of the resulting noninteracting propagator, provides a possible gen...

This paper compares the classical concept of assumed density lters (ADF) with a new class of approximate lters, the projection lters (PF). It is shown that the concept of ADF is inconsistent in the sense that the resulting lters vary according to the choice of a stochastic calculus, i.e. It^ o or McShane{Fisk{Stratonovich (MFS). The PF are based on the diierential geometric approach to statisti...

We study a class of singularly perturbed dynamical systems that have fast and slow components, 1 being the fast to slow timescale ratio. The fast components are governed by a strongly mixing discrete map, which is iterated at time intervals . The slow components are governed by a /rst-order /nite-di0erence equation that uses a time step . As tends to zero, the fast components may be eliminated,...

The many-body dynamics of a quantum computer can be reduced to the time evolution of non-interacting quantum bits in auxiliary fields by use of the Hubbard-Stratonovich representation of two-bit quantum gates in terms of one-bit gates. This makes it possible to perform the stochastic simulation of a quantum algorithm, based on the Monte Carlo evaluation of an integral of dimension polynomial in...

In this article we establish a large deviation principle for the family {ν ε : ε ∈ (0, 1)} of distributions of the scaled stochastic processes {P − log √ ε Z t } t≤1 , where (Z t) t∈[0,1] is a square-integrable martingale over Brownian filtration and (P t) t≥0 is the Ornstein-Uhlenbeck semigroup. The rate function is identified as well in terms of the Wiener-Itô chaos decomposition of the termi...

Abstract. In this article we establish a substitution theorem for semilinear stochastic evolution equations (see’s) depending on the initial condition as an infinite-dimensional parameter. Due to the infinitedimensionality of the initial conditions and of the stochastic dynamics, existing finite-dimensional results do not apply. The substitution theorem is proved using Malliavin calculus techni...

This paper studies the stochastic heat equation with multiplicative noises: ∂u ∂t = 1 2 ∆u+uẆ , where Ẇ is a mean zero Gaussian noise and uẆ is interpreted both in the sense of Skorohod and Stratonovich. The existence and uniqueness of the solution are studied for noises with general time and spatial covariance structure. Feynman-Kac formulas for the solutions and for the moments of the solutio...