Second order elliptic partial differential equations driven by Lévy white noise
نویسندگان
چکیده
This paper deals with linear stochastic partial differential equations variable coefficients driven by Lévy white noise. First, an existence theorem for integral transforms of noise is derived and the generalized mild solutions second order elliptic proved. Further, electric Schrödinger operator different potential functions V discussed.
منابع مشابه
Stochastic Partial Differential Equations Driven by Lévy Space - Time White Noise
In this paper we develop a white noise framework for the study of stochastic partial differential equations driven by a d-parameter (pure jump) Lévy white noise. As an example we use this theory to solve the stochastic Poisson equation with respect to Lévy white noise for any dimension d. The solution is a stochastic distribution process given explicitly. We also show that if d ≤ 3, then this s...
متن کاملCoupling for some partial differential equations driven by white noise
We prove, using coupling arguments, exponential convergence to equilibrium for reaction–diffusion and Burgers equations driven by space-time white noise. We use a coupling by reflection. 2000 Mathematics Subject Classification: 60H15, 35K57, 35Q53
متن کاملStochastic Partial Differential Equations Driven by Purely Spatial Noise
We study bilinear stochastic parabolic and elliptic PDEs driven by purely spatial white noise. Even the simplest equations driven by this noise often do not have a square-integrable solution and must be solved in special weighted spaces. We demonstrate that the Cameron–Martin version of the Wiener chaos decomposition is an effective tool to study both stationary and evolution equations driven b...
متن کامل8 Stochastic Partial Differential Equations Driven by Purely Spatial Noise
We study bilinear stochastic parabolic and elliptic PDEs driven by purely spatial white noise. Even the simplest equations driven by this noise often do not have a square-integrable solution and must be solved in special weighted spaces. We demonstrate that the Cameron-Martin version of the Wiener chaos decomposition is an effective tool to study both stationary and evolution equations driven b...
متن کاملDiv First-Order System LL* (FOSLL*) for Second-Order Elliptic Partial Differential Equations
The first-order system LL* (FOSLL*) approach for general second-order elliptic partial differential equations was proposed and analyzed in [Z. Cai et al., SIAM J. Numer. Anal., 39 (2001), pp. 1418–1445], in order to retain the full efficiency of the L2 norm first-order system leastsquares (FOSLS) approach while exhibiting the generality of the inverse-norm FOSLS approach. The FOSLL* approach of...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Modern stochastics: theory and applications
سال: 2021
ISSN: ['2351-6046', '2351-6054']
DOI: https://doi.org/10.15559/21-vmsta181