A degenerate stochastic partial differential equation for superprocesses with singular interaction
نویسندگان
چکیده
The scaling limit for a class of interacting superprocesses and the associated singular, degenerate stochastic partial differential equation (SDSPDE) are investigated. It is proved that the scaling limit is a coalescing, purely-atomic-measure-valued process which is the unique strong solution of a reconstructed, associated SDSPDE.
منابع مشابه
A Compact Scheme for a Partial Integro-Differential Equation with Weakly Singular Kernel
Compact finite difference scheme is applied for a partial integro-differential equation with a weakly singular kernel. The product trapezoidal method is applied for discretization of the integral term. The order of accuracy in space and time is , where . Stability and convergence in norm are discussed through energy method. Numerical examples are provided to confirm the theoretical prediction ...
متن کاملSimulation of Singular Fourth- Order Partial Differential Equations Using the Fourier Transform Combined With Variational Iteration Method
In this paper, we present a comparative study between the modified variational iteration method (MVIM) and a hybrid of Fourier transform and variational iteration method (FTVIM). The study outlines the efficiencyand convergence of the two methods. The analysis is illustrated by investigating four singular partial differential equations with variable coefficients. The solution of singular partia...
متن کاملFinite difference method for solving partial integro-differential equations
In this paper, we have introduced a new method for solving a class of the partial integro-differential equation with the singular kernel by using the finite difference method. First, we employing an algorithm for solving the problem based on the Crank-Nicholson scheme with given conditions. Furthermore, we discrete the singular integral for solving of the problem. Also, the numerical results ob...
متن کاملNumerical Solution of Weakly Singular Ito-Volterra Integral Equations via Operational Matrix Method based on Euler Polynomials
Introduction Many problems which appear in different sciences such as physics, engineering, biology, applied mathematics and different branches can be modeled by using deterministic integral equations. Weakly singular integral equation is one of the principle type of integral equations which was introduced by Abel for the first time. These problems are often dependent on a noise source which a...
متن کاملThe Burgers Superprocess
We define the Burgers superprocess to be the solution of the stochastic partial differential equation ∂ ∂t u(t, x) =∆u(t, x) − λu(t, x)∇u(t, x) + γ √ u(t, x) W (dt, dx), where t ≥ 0, x ∈ R, and W is space-time white noise. Taking γ = 0 gives the classic Burgers equation, an important, non-linear, partial differential equation. Taking λ = 0 gives the super Brownian motion, an important, measure ...
متن کامل