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Then we strengthen this convergence by deriving suitable fractional Sobolev compactness estimates. As a by-product, our main result allows us to obtain asymptotic results for a class of piecewise constant stochastic processes with memory.<\/jats:p>","DOI":"10.1137\/19m1240721","type":"journal-article","created":{"date-parts":[[2020,5,5]],"date-time":"2020-05-05T14:18:16Z","timestamp":1588688296000},"page":"2275-2312","source":"Crossref","is-referenced-by-count":1,"title":["Self-Similar Behavior of a Nonlocal Diffusion Equation with Time Delay"],"prefix":"10.1137","volume":"52","author":[{"given":"Arnaud","family":"Ducrot","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alexandre","family":"Genadot","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2020,5,5]]},"reference":[{"key":"atypb1","first-page":"161","volume":"35","author":"Amann H.","year":"2000","journal-title":"Glas. Mat. Ser. 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