In this talk we present a survey of recent advances considering convergence of polygonal line processes constructed from partial sums of random elements with values in perhaps in nite dimensional sample space. Although several topological frameworks shall be considered the main attention is paid to Holder spaces as paths spaces for polygonal lines. We also discuss applications to statistics emphasizing problems of changed segment in a sample.
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Conference proceedings should be sent to Prof. Hab. Dr. Vygantas Paulauskas at vygantas.paulauskas@mif.vu.lt until September 1st.