The Probabilistic Evaluation Of Certain Partial Nested Multiple Integrals

The probabilistic evaluation of multiple integrals is a classical problem of classical analysis. The probabilistic evaluation of nested multiple integrals is not only related to the distribution of order statistics in the probability theory but also related to count of young tableaux in the combinatorial mathematics.In this paper, using the tools of probability theory to discuss the problem of probabilistic evaluation of the certain partial nested multiple integrals. The first chapter introduce the research background, status and research thought. The second chapter is the preliminary knowledge of this paper. The first part are definitions and symbols used in this paper, and the next are some important properties of order statistic and the counting formula of the standard Young table.The third chapter is the main part of this paper. Firstly, we study the results of multiple integrals in two special circumstances(k=1and k=n), here In,k=∫∫…∫Jn,k(n!)3dx1…dxndy1…dyndt1…dtn and Jn,k is a nested interval. Secondly, using the tools and methods of probability, calculate the results of the multiple integrals when k=2,3and4. Finally, we simplified the results into a relatively simple form.