Large Deviation Probabilities for Sums of Independent Random Variables

2013 ◽  
pp. 239-276
Author(s):  
Alexandr A. Borovkov
Keyword(s):  
Large Deviation ◽  
Random Variables ◽  
Independent Random Variables ◽  
Large Deviation Probabilities

scholarly journals The Strong Law of Large Numbers for Extended Negatively Dependent Random Variables

2010 ◽  
Vol 47 (04) ◽  
pp. 908-922 ◽  
Author(s):  
Yiqing Chen ◽  
Anyue Chen ◽  
Kai W. Ng
Keyword(s):  
Law Of Large Numbers ◽  
Large Deviation ◽  
Random Variables ◽  
Renewal Theory ◽  
Independent Random Variables ◽  
Strong Law ◽  
Finite Dimensional ◽  
Negatively Dependent Random Variables ◽  
Large Numbers ◽  
New Inequalities

A sequence of random variables is said to be extended negatively dependent (END) if the tails of its finite-dimensional distributions in the lower-left and upper-right corners are dominated by a multiple of the tails of the corresponding finite-dimensional distributions of a sequence of independent random variables with the same marginal distributions. The goal of this paper is to establish the strong law of large numbers for a sequence of END and identically distributed random variables. In doing so we derive some new inequalities of large deviation type for the sums of END and identically distributed random variables being suitably truncated. We also show applications of our main result to risk theory and renewal theory.

scholarly journals Sharp large deviation results for sums of independent random variables

2015 ◽  
Vol 58 (9) ◽  
pp. 1939-1958 ◽  
Author(s):  
XieQuan Fan ◽  
Ion Grama ◽  
QuanSheng Liu
Keyword(s):  
Large Deviation ◽  
Random Variables ◽  
Independent Random Variables ◽  
Sharp Large Deviation

Positive exponent in families with flat critical point

1999 ◽  
Vol 19 (3) ◽  
pp. 767-807 ◽  
Author(s):  
HANS THUNBERG
Keyword(s):  
Critical Point ◽  
Finite Order ◽  
Parameter Space ◽  
Positive Measure ◽  
Large Deviation ◽  
Random Variables ◽  
Independent Random Variables ◽  
Unimodal Maps ◽  
Key Points ◽  
Positive Exponent

It is known that in generic, full unimodal families with a critical point of finite order, there exists a set of positive measure in parameter space such that the corresponding maps have chaotic behaviour. In this paper we prove the corresponding statement for certain families of unimodal maps with flat critical point. One of the key-points is a large deviation argument for sums of ‘almost’ independent random variables with only finitely many moments.

scholarly journals Exact Lower Bounds on the Exponential Moments of Truncated Random Variables

2011 ◽  
Vol 48 (02) ◽  
pp. 547-560 ◽  
Author(s):  
Iosif Pinelis
Keyword(s):  
Option Pricing ◽  
Lower Bounds ◽  
Large Deviation ◽  
Asymptotic Properties ◽  
Random Variables ◽  
Random Variable ◽  
Exponential Moments ◽  
Comparative Advantages ◽  
Large Deviation Probabilities

Exact lower bounds on the exponential moments of min(y,X) andX1{X<y} are provided given the first two moments of a random variableX. These bounds are useful in work on large deviation probabilities and nonuniform Berry-Esseen bounds, when the Cramér tilt transform may be employed. Asymptotic properties of these lower bounds are presented. Comparative advantages of the so-called Winsorization min(y,X) over the truncationX1{X<y} are demonstrated. An application to option pricing is given.

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