An extension of P-113, Random Walk, Scattering, and Invariant Imbedding-I: One-dimensional Discrete Case, which applies the techniques of invariant imbedding to various random-walk processes and to questions of scattering theory. The present paper shows how the ideas presented in the earlier study enable multidimensional, time-dependent, and energy-dependent processes to be treated. A remarkable formal equivalence holds in all of these cases, with the result that the same equations occur repeatedly in different variables. Both new analytic and new computational approaches are achieved. Only the discrete versions of these processes are considered. 19 pp.
This report is part of the RAND Corporation Paper series. The paper was a product of the RAND Corporation from 1948 to 2003 that captured speeches, memorials, and derivative research, usually prepared on authors' own time and meant to be the scholarly or scientific contribution of individual authors to their professional fields. Papers were less formal than reports and did not require rigorous peer review.
Our mission to help improve policy and decisionmaking through research and analysis is enabled through our core values of quality and objectivity and our unwavering commitment to the highest level of integrity and ethical behavior. To help ensure our research and analysis are rigorous, objective, and nonpartisan, we subject our research publications to a robust and exacting quality-assurance process; avoid both the appearance and reality of financial and other conflicts of interest through staff training, project screening, and a policy of mandatory disclosure; and pursue transparency in our research engagements through our commitment to the open publication of our research findings and recommendations, disclosure of the source of funding of published research, and policies to ensure intellectual independence. For more information, visit www.rand.org/about/principles.
The RAND Corporation is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.