Scholarlink

<p>We solve two continuous extremal problems on the classes of monotone functions: in the first problem, we find extremal values for a line integral of a coordinate-wise monotone function of two variables from a rearrangement-invariant class of functions; in the second one, we find extremal values for the expectation of a random process with monotone trajectories at a random time. In both cases, we reduce the continuous problems to their discrete counterparts. The obtained discrete problems are, on the one hand, interesting on their own and, on the other hand, give a natural explanation of the structure of the extremal functions for the continuous problems.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

On discretization of some extremal problems

  • 期刊论文

  • 发表日期：

    2025年11月1日

查看全文
  • Oleg Kovalenko

摘要

We solve two continuous extremal problems on the classes of monotone functions: in the first problem, we find extremal values for a line integral of a coordinate-wise monotone function of two variables from a rearrangement-invariant class of functions; in the second one, we find extremal values for the expectation of a random process with monotone trajectories at a random time. In both cases, we reduce the continuous problems to their discrete counterparts. The obtained discrete problems are, on the one hand, interesting on their own and, on the other hand, give a natural explanation of the structure of the extremal functions for the continuous problems.