A Local Limit Theorem and Recurrence Conditions for Sums of Independent Non-Lattice Random Variables

A Local Limit Theorem for Sums of Dependent Random Variables

A version of central limit is established normalized sums dependent random when a theorem is and conditional are sufficiently The proof ideas from by representing density as integral of score function a translation of distributions. 1980 Subject 60F99.

A Local Limit Theorem for Sums of Independent Random Vectors

We prove a local limit theorem for sums of independent random vectors satisfying appropriate tightness assumptions. In particular, the local limit theorem holds in dimension 1 if the summands are uniformly bounded.

On the Lower Limit of Sums of Independent Random Variables

1. Let X1 , X2 , • • • , Xn . . . be independent random variables and let Sn = X, . In the so-called law of the iterated logarithm, completely solved by Feller recently, the upper limit of S n as n -4 co is considered and its true order of magnitude is found with probability one . A counterpart to that problem is to consider the lower limit of Sn as n --> oo and to make a statement about its or...

Central and Local Limit Theories in Markov Dependent Random Variables

Limit Theorem for Sums of Random Products

We study asymptotic behavior of the sums ZN,m(β) determined by the formula ZN,m(β) = N