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Abstract Let {Xi}i≥1 be independent, identically distributed random vectors in ℤd,d≥1. Let LLn(x)≡ℙ(Sn=x),n≥1,x∈ℤd, be the likelihood function for Sn=∑i=1nXi. For integers j≥2 and n≥1, let an(j)≡∑x∈ℤd(Ln(x))j. We show that if… Click to show full abstract
Abstract Let {Xi}i≥1 be independent, identically distributed random vectors in ℤd,d≥1. Let LLn(x)≡ℙ(Sn=x),n≥1,x∈ℤd, be the likelihood function for Sn=∑i=1nXi. For integers j≥2 and n≥1, let an(j)≡∑x∈ℤd(Ln(x))j. We show that if X1-X2 has a nondegenerate aperiodic distribution in ℤd and ????(∥X1∥2)>∞, then limn→∞n(j-1)d∕2an(j)≡a(j,d) exists and 0
Keywords:
powers likelihood;
random walks;
functions random;
likelihood functions
Journal Title: Advances in Applied Probability
Year Published: 2018
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Journal Title: Advances in Applied Probability
Year Published: 2018
Link to full text (if available)
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recommendations!