Continuous dependence estimate for conservation laws with L\'{e}vy noise
Analysis of PDEs
2015-02-10 v1
Abstract
We are concerned with multidimensional stochastic balance laws driven by L\'{e}vy processes. Using bounded variation (BV) estimates for vanishing viscosity approximations, we derive an explicit continuous dependence estimate on the nonlinearities of the entropy solutions under the assumption that L\'{e}vy noise only depends on the solution. This result is used to show the error estimate for the stochastic vanishing viscosity method. In addition, we establish fractional estimate for vanishing viscosity approximations in case the noise coefficient depends on both the solution and spatial variable.
Cite
@article{arxiv.1502.02490,
title = {Continuous dependence estimate for conservation laws with L\'{e}vy noise},
author = {Imran H. Biswas and Ujjwal Koley and Ananta K. Majee},
journal= {arXiv preprint arXiv:1502.02490},
year = {2015}
}
Comments
29 pages