# How can I calculate distribution of minima of sections of a continuous path (from a stochastic process)?

I have a long slab whose width is defined by a stochastic process, whose complete statistics I am aware of, say. I now cut it into smaller sections of uniform length, and calculate the minimum width in each section. How do I find out the statistics of the minimum widths of the sections?

You may assume that the slab widths come from a process with a rectangular power spectral density (if that helps).

I understand this amounts to non-linear sampling, and for first-order approximations, have tried to model the process using Markov matrices, but is there a complete way to solve this problem?

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