38 research outputs found
Local–Global Minimum Property in Unconstrained Minimization Problems
The main goal of this paper is to prove some new results and extend some
earlier ones about functions, which possess the so called local-global minimum property.
In the last section, we show an application of these in the theory of calculus of
variations
Random means generated by random variables: expectation and limit theorems
We introduce the notion of a random mean generated by a random variable and
give a construction of its expected value. We derive some sufficient conditions
under which strong law of large numbers and some limit theorems hold for random
means generated by the elements of a sequence of independent and identically
distributed random variables.Comment: 25 page
Limit theorems for Bajraktarevi\'c and Cauchy quotient means of independent identically distributed random variables
We derive strong law of large numbers and central limit theorems for
Bajraktarevi\'c, Gini and exponential- (also called Beta-type) and logarithmic
Cauchy quotient means of independent identically distributed (i.i.d.) random
variables. The exponential- and logarithmic Cauchy quotient means of a sequence
of i.i.d. random variables behave asymptotically normal with the usual square
root scaling just like the geometric means of the given random variables.
Somewhat surprisingly, the multiplicative Cauchy quotient means of i.i.d.
random variables behave asymptotically in a rather different way: in order to
get a non-trivial normal limit distribution a time dependent centering is
needed.Comment: 25 page
Homogeneity properties of subadditive functions
We collect, supplement and extend some well-known basic facts on various
homogeneity properties of subadditive functions.
Key Words: Homogeneous and subadditive functions, seminorms and pre-
seminorms.
AMS Classification Number: 39B7
Limit theorems for Bajraktarevic and Cauchy quotient means of independent identically distributed random variables
We derive strong laws of large numbers and central limit theorems for Bajraktarevic, Gini and exponential- (also called Beta-type) and logarithmic Cauchy quotient means of independent identically distributed (i.i.d.) random variables. The exponential- and logarithmic Cauchy quotient means of a sequence of i.i.d. random variables behave asymptotically normal with the usual square root scaling just like the geometric means of the given random variables. Somewhat surprisingly, the multiplicative Cauchy quotient means of i.i.d. random variables behave asymptotically in a rather different way: in order to get a non-trivial normal limit distribution a time dependent centering is needed