A Note on Nonrecurrent Random Walks1
نویسنده
چکیده
Let {Xi},i = l, • • • , be a sequence of independent and identically distributed random variables with density function f(x). We shall assume throughout that EXi=p>0. Let {Sn}, n = l, • • • , be the sequence of cumulative sums Sn= 23"-1 -^«'Let H(x) = 23»= i P(Sn ^x) and h(x)=H'(x). Since H(x) is nondecreasing, h(x) is defined for almost all x. Let A be any Borel set of positive real numbers and m(A) denote its Lebesgue measure. Chung and Derman [2] proved that
منابع مشابه
Moderate Deviations and Law of the Iterated Logarithm for Intersections of the Ranges of Random Walks1 By
متن کامل
SECOND-ORDER FLUCTUATIONS AND CURRENT ACROSS CHARACTERISTIC FOR A ONE-DIMENSIONAL GROWTH MODEL OF INDEPENDENT RANDOM WALKS1 BY TIMO SEPPÄLÄINEN University of Wisconsin
Fluctuations from a hydrodynamic limit of a one-dimensional asymmetric system come at two levels. On the central limit scale n1/2 one sees initial fluctuations transported along characteristics and no dynamical noise. The second order of fluctuations comes from the particle current across the characteristic. For a system made up of independent random walks we show that the second-order fluctuat...
متن کاملRecurrence Equations for the Probability Distribution of Sample Configurations in Exact Population Genetics Models
Recurrence equations for the number of types and the frequency of each type in a random sample drawn from a finite population undergoing discrete, nonoverlapping generations and reproducing according to the Cannings exchangeable model are deduced under the assumption of a mutation scheme with infinitely many types. The case of overlapping generations in discrete time is also considered. The equ...
متن کاملA Note on the Strong Law of Large Numbers
Petrov (1996) proved the connection between general moment conditions and the applicability of the strong law of large numbers to a sequence of pairwise independent and identically distributed random variables. This note examines this connection to a sequence of pairwise negative quadrant dependent (NQD) and identically distributed random variables. As a consequence of the main theorem ...
متن کاملA Rare Variation of Inferior Laryngeal Nerve: Nonrecurrent Laryngeal Nerve.
A nonrecurrent laryngeal nerve variant of the inferior laryngeal nerve is very rarely seen, and surgeons should keep it in mind during thyroid surgery. Preoperative findings, like situs invertus and dysphagia lusoria, may be suggestive of a nonrecurrent laryngeal nerve. However, these findings always have not to be together with nonrecurrent laryngeal nerve, like our case.
متن کامل