THE HIGHER ORDER LARGE-DEVIATION APPROXIMATION FOR THE DISTRIBUTION OF THE SUM OF INDEPENDENT DISCRETE RANDOM VARIABLES

2003 ◽  
pp. 558-579 ◽  
Author(s):  
Masafumi Akahira ◽  
Kei Takeuchi ◽  
Kunihiko Takahashi
Keyword(s):  
Large Deviation ◽  
Random Variables ◽  
Higher Order ◽  
Discrete Random Variables

scholarly journals Application of the Kusuoka approximation with a tree-based branching algorithm to the pricing of interest-rate derivatives under the HJM model

2010 ◽  
Vol 13 ◽  
pp. 208-221 ◽  
Author(s):  
Mariko Ninomiya
Keyword(s):  
Interest Rate ◽  
Random Variables ◽  
Factor Models ◽  
Higher Order ◽  
Weak Approximation ◽  
Interest Rate Derivatives ◽  
Hjm Model ◽  
Discrete Random Variables

AbstractThis paper demonstrates the application of a new higher-order weak approximation, called the Kusuoka approximation, with discrete random variables to non-commutative multi-factor models. Our experiments show that using the Heath–Jarrow–Morton model to price interest-rate derivatives can be practically feasible if the Kusuoka approximation is used along with the tree-based branching algorithm.

Large deviation theorems for weighted sums applied to a geographical problem

2002 ◽  
Vol 39 (2) ◽  
pp. 251-260 ◽  
Author(s):  
Olivier Bonin
Keyword(s):  
Large Deviation ◽  
Random Variables ◽  
Weighted Sums ◽  
Travel Times ◽  
Discrete Random Variables ◽  
The Impact

A large deviation expansion is used to evaluate the impact of errors in a geographical database on the computation of travel times. We work in the framework of discrete random variables and improve a theorem by Book to solve this problem. Simulations are provided to illustrate the methodology.

Large deviation theorems for weighted sums applied to a geographical problem

2002 ◽  
Vol 39 (02) ◽  
pp. 251-260 ◽  
Author(s):  
Olivier Bonin
Keyword(s):  
Large Deviation ◽  
Random Variables ◽  
Weighted Sums ◽  
Travel Times ◽  
Discrete Random Variables ◽  
The Impact

A large deviation expansion is used to evaluate the impact of errors in a geographical database on the computation of travel times. We work in the framework of discrete random variables and improve a theorem by Book to solve this problem. Simulations are provided to illustrate the methodology.

Normal approximations to discrete unimodal distributions

1986 ◽  
Vol 23 (04) ◽  
pp. 1013-1018
Author(s):  
B. G. Quinn ◽  
H. L. MacGillivray
Keyword(s):  
Stationary Distribution ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Hypergeometric Distribution ◽  
Death Process ◽  
Normal Approximations ◽  
Discrete Random Variables ◽  
Birth Death

Sufficient conditions are presented for the limiting normality of sequences of discrete random variables possessing unimodal distributions. The conditions are applied to obtain normal approximations directly for the hypergeometric distribution and the stationary distribution of a special birth-death process.

scholarly journals The number of failed components in a coherent working system when the lifetimes are discretely distributed

Metrika ◽  
2021 ◽  
Author(s):  
Krzysztof Jasiński
Keyword(s):  
Random Variables ◽  
Continuous Case ◽  
Coherent System ◽  
Coherent Systems ◽  
Discrete Random Variables ◽  
Independent And Identically Distributed

AbstractIn this paper, we study the number of failed components of a coherent system. We consider the case when the component lifetimes are discrete random variables that may be dependent and non-identically distributed. Firstly, we compute the probability that there are exactly i, $$i=0,\ldots ,n-k,$$ i = 0 , … , n - k , failures in a k-out-of-n system under the condition that it is operating at time t. Next, we extend this result to other coherent systems. In addition, we show that, in the most popular model of independent and identically distributed component lifetimes, the obtained probability corresponds to the respective one derived in the continuous case and existing in the literature.

Two-stage stochastic programming problems involving interval discrete random variables

OPSEARCH ◽  
2012 ◽  
Vol 49 (3) ◽  
pp. 280-298 ◽  
Author(s):  
Suresh Kumar Barik ◽  
Mahendra Prasad Biswal ◽  
Debashish Chakravarty
Keyword(s):  
Stochastic Programming ◽  
Random Variables ◽  
Two Stage ◽  
Discrete Random Variables

scholarly journals Chover-Type Laws of the Iterated Logarithm for Kesten-Spitzer Random Walks in Random Sceneries Belonging to the Domain of Stable Attraction

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Wensheng Wang ◽  
Anwei Zhu
Keyword(s):  
Random Walk ◽  
Large Deviation ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Domain Of Attraction ◽  
Stable Law ◽  
Iterated Logarithm ◽  
Cluster Set ◽  
Random Scenery ◽  
Unique Integer

Let X={Xi,i≥1} be a sequence of real valued random variables, S0=0 and Sk=∑i=1kXi  (k≥1). Let σ={σ(x),x∈Z} be a sequence of real valued random variables which are independent of X’s. Denote by Kn=∑k=0nσ(⌊Sk⌋)  (n≥0) Kesten-Spitzer random walk in random scenery, where ⌊a⌋ means the unique integer satisfying ⌊a⌋≤a<⌊a⌋+1. It is assumed that σ’s belong to the domain of attraction of a stable law with index 0<β<2. In this paper, by employing conditional argument, we investigate large deviation inequalities, some sufficient conditions for Chover-type laws of the iterated logarithm and the cluster set for random walk in random scenery Kn. The obtained results supplement to some corresponding results in the literature.

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