Few analytical methods exist for quantitative studies of large fluctuations in stochastic systems. In this article, we develop a simple diagrammatic approach to the Chemical Master Equation that allows us to calculate multi-time correlation functions which are accurate to a any desired order in van Kampen’s system size expansion. Specifically, we present a set of Feynman rules from which this d...

This paper presents two approaches to characterize the dynamics of weight space probability density starting from a master equation. In the rst, we provide a class of algorithms for which an exact evaluation of the integrals in the master equation is possible. This enables the time evolution of the density to be calculated at each time step without approximation. In the second, we expand earlie...

A two-space dimensional heat equation perturbed by a white noise driven in a bounded volume is considered. The equation is perturbed by a non-linearity of the type : f(AU) :, where : : means Wick (re)ordering with respect to the free solution; ; A are small parameters , U denotes a solution, f is the Fourier transform of a complex measure with compact support. Existence and uniqueness of the so...

PURPOSE The purpose of this paper is to implement a noise-weighted filtered backprojection (FBP) algorithm in the form of "convolution" backprojection, but this "convolution" has a spatially variant integration kernel. METHODS Noise-weighted FBP algorithms have been developed in recent years, with filtering being performed in the Fourier domain. The noise weighting makes the ramp filter in th...

This paper presents two approaches to characterize the dynamics of weight space probability density starting from a master equation In the rst we provide a class of algorithms for which an exact evaluation of the integrals in the master equation is possible This enables the time evolution of the density to be calculated at each time step without approximation In the second we expand earlier wor...

In the recent years Schrödinger problem has gained a lot of attention because connection, in small-noise regime, with Monge-Kantorovich optimal transport problem. Its value, entropic cost C T , is here deeply investigated. this paper we study regularity respect to parameter under curvature condition and explicitly compute its first second derivative. As applications: - determine large-time limi...