Executive Summary : | The study of nonlinear stochastic partial differential equations (SPDEs) is necessitated by the attempts to under- stand/describe a large number of physical processes where uncertainty/randomness is an integral phenomenon. A systematic mathematical understanding of SPDEs would surely lead to better understanding of the underlying physical process. In the recent decades, the broader area of SPDEs has attracted the attention of many and research on this subject has progressed steadily. We also have had our interest firmly lodged in this subject and hyperbolic conservation laws with noise has been our primary focus. Over the last few years, a substantial part of our effort has been to investigate questions related to wellposedness, stability and regularity of stochastic entropy solutions of such problems. We have had our fair share of success resulting from these efforts and our research on this topic is recognised by the international community. With an in-depth knowledge and expertise on the subject, we want to broaden our horizon and delve into the aspects of numerical schemes for such problems. We are particularly interested in fully discrete monotone schemes for stochastic conservation laws. While there are recent results on convergence of such schemes, we wish to push the envelope by providing robust convergence analysis and estimating the rate of convergence of such schemes. |