A new derivation of the quantum Boltzmann transport equation for the Fermion system from the quantum time evolution equation for the wigner distribution function is presented. The method exhibits the origin of the time - irreversibility of the Boltzmann equation. In the present work, the spin dependent and indistinguishibility of particles are also considered.

We provide a Frobenius type existence result for finite-dimensional invariant submanifolds for stochastic equations in infinite dimension, in the spirit of Da Prato and Zabczyk [5]. We recapture and make use of the convenient calculus on Fréchet spaces, as developed by Kriegl and Michor [16]. Our main result is a weak version of the Frobenius theorem on Fréchet spaces. As an application we char...

We describe Stochastic Loewner Evolution on arbitrary Riemann surfaces with boundary using Conformal Field Theory methods. We propose in particular a CFT construction for a probability measure on (clouded) paths, and check it against known restriction properties. The probability measure can be thought of as a section of the determinant bundle over moduli spaces of Riemann surfaces. Loewner evol...

We consider an optimal control problem for a Hilbert space valued linear stochastic evolution equation with additive noise and a quadratic goal function in integral form. We solve an innnite dimensional linear stochastic regulator problem by applying an augmented Lagrangian algorithm. Because of high amounts of computation time required by numerical solution of such problems we investigate a pa...

It is shown that the evolution of the density perturbations during certain eras of substantial entropy generation in the universe can be described in the scheme of the KPZ equation. Therefore, the in uence on cosmological structure formation by stochastic forces arising from various dissipations can be studied through the universal characteristics of surface growth in d = 3 + 1 dimensions. We i...

For a large class of stochastic processes, the evolution of the underlying probability density function is prescribed by a forward Kolmogorov equation, also called FokkerPlanck equation, a second-order parabolic partial differential equation. In this manner, an optimal control problem subject to an Itô stochastic differential equation can be rendered deterministic by recasting it as an optimal ...

It is shown that the evolution of the density perturbations during certain eras of substantial entropy generation in the universe can be described in the scheme of the KPZ equation. Therefore, the influence on cosmological structure formation by stochastic forces arising from various dissipations can be studied through the universal characteristics of surface growth in d = 3 + 1 dimensions. We ...

We show that the fluctuation-dissipation relation can be established for a class of stochastic dynamics that lack detailed balance. This class comprises lattice spin models whose time evolution is governed by a master equation with a one-spin-flip transition rate having the up-down symmetry. The relation is obtained by the introduction of a multiplicative perturbation of the transition rate, wh...

This work faces the problem of the origin of the logarithmic character of the Gompertzian growth. We show that the macroscopic, deterministic Gompertz equation describes the evolution from the initial state to the final stationary value of the median of a log-normally distributed, stochastic process. Moreover, by exploiting a stochastic variational principle, we account for self-regulating feat...

In this paper, we consider a class of semilinear stochastic evolution equations on Hilbert space driven by a stochastic vector measure. The nonlinear terms are assumed to be merely continuous and bounded on bounded sets. We prove the existence of measure valued solutions generalizing some earlier results of the author. As a corollary, an existence result of a measure solution for a forward Kolm...