{"paper":{"title":"Least Energy Approximation for Processes with Stationary Increments","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.PR","authors_text":"Mikhail Lifshits, Zakhar Kabluchko","submitted_at":"2015-06-28T07:14:00Z","abstract_excerpt":"A function $f=f_T$ is called least energy approximation to a function $B$ on the interval $[0,T]$ with penalty $Q$ if it solves the variational problem $$ \\int_0^T \\left[ f'(t)^2 + Q(f(t)-B(t)) \\right] dt \\searrow \\min. $$ For quadratic penalty the least energy approximation can be found explicitly. If $B$ is a random process with stationary increments, then on large intervals $f_T$ also is close to a process of the same class and the relation between the corresponding spectral measures can be found. We show that in a long run (when $T\\to \\infty$) the expectation of energy of optimal approxima"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.08369","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}