Moments for the parabolic Anderson model: on a result by Hu and Nualart
نویسنده
چکیده
Abstract We consider the Parabolic Anderson Model ∂tu = Lu + uẆ , where L is the generator of a Lévy Process and Ẇ is a white noise in time, possibly correlated in space. We present an alternate proof and an extension to a result by Hu and Nualart ([14]) giving explicit expressions for moments of the solution. We do not consider a Feynman-Kac representation, but rather make a recursive use of Itô’s formula.
منابع مشابه
Neural Network Performance Analysis for Real Time Hand Gesture Tracking Based on Hu Moment and Hybrid Features
This paper presents a comparison study between the multilayer perceptron (MLP) and radial basis function (RBF) neural networks with supervised learning and back propagation algorithm to track hand gestures. Both networks have two output classes which are hand and face. Skin is detected by a regional based algorithm in the image, and then networks are applied on video sequences frame by frame in...
متن کاملMoments of 2d Parabolic Anderson Model
In this note, we use the Feynman-Kac formula to derive a moment representation for the 2D parabolic Anderson model in small time, which is related to the intersection local time of planar Brownian motions.
متن کاملMoments and Growth Indices for the Nonlinear Stochastic Heat Equation with Rough Initial Conditions1 by Le Chen
We study the nonlinear stochastic heat equation in the spatial domain R, driven by space–time white noise. A central special case is the parabolic Anderson model. The initial condition is taken to be a measure on R, such as the Dirac delta function, but this measure may also have noncompact support and even be nontempered (e.g., with exponentially growing tails). Existence and uniqueness of a r...
متن کاملStock Market Bubbles and Business Cycles: A DSGE Model for the Iranian Economy
T his paper investigates the movement between stock market bubbles and fluctuations in aggregate variables within a DSGE model for the Iranian economy. We apply a new Keynesian monetary framework with nominal rigidity in wages and prices based on the study by Ikeda (2013), which is developed with appropriate framework for the Iranian economy. We consider central bank behavior differe...
متن کاملMARKOV FIELD PROPERTIES OF SOLUTIONS OF WHITE NOISE DRIVEN QUASI-LINEAR PARABOLIC PDEs
In this paper we study a one-dimensional quasi-linear parabolic stochastic partial differential equation driven by a space-time white noise. First the germ Markov field property is proved for the solution of a Cauchy problem for this equation. Secondly, we introduce periodic (in time) boundary conditions and we study the existence and uniqueness of a solution and its Markov properties. The main...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011