Sudakov's typical marginals, random linear functionals and a conditional central limit theorem

1997 ◽  
Vol 107 (3) ◽  
pp. 313-324 ◽  
Author(s):  
Heinrich von Weizsäcker
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Linear Functionals ◽  
Conditional Central Limit Theorem

scholarly journals Second-Order Approximation in the Conditional Central Limit Theorem

1986 ◽  
Vol 14 (1) ◽  
pp. 313-325 ◽  
Author(s):  
Dieter Landers ◽  
Lothar Rogge
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Order Approximation ◽  
Second Order ◽  
Second Order Approximation ◽  
Conditional Central Limit Theorem

scholarly journals Remainder term estimates in a conditional central limit theorem for integer-valued random variables

1985 ◽  
Vol 39 (1) ◽  
pp. 75-85 ◽  
Author(s):  
M. P. Quine
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Remainder Term ◽  
Conditional Distribution ◽  
Finite Population ◽  
Random Variables ◽  
Weighted Sum ◽  
Type Result ◽  
Conditional Central Limit Theorem

AbstractA Berry-Esseen type result is given for the conditional distribution of a weighted sum of i.i.d. integer-valued r.v.'s given that their unweighted sum equals its expectation. The examples include the case of sampling without replacement from a finite population.

scholarly journals Nonuniform Estimates in the Conditional Central Limit Theorem

1987 ◽  
Vol 15 (2) ◽  
pp. 776-782 ◽  
Author(s):  
Dieter Landers ◽  
Lothar Rogge
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Conditional Central Limit Theorem

Conditional Central Limit Theorem

2017 ◽  
Vol 61 (4) ◽  
pp. 613-631
Author(s):  
A. V. Bulinski
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Conditional Central Limit Theorem

scholarly journals The conditional central limit theorem in Hilbert spaces

2003 ◽  
Vol 108 (2) ◽  
pp. 229-262 ◽  
Author(s):  
Jérôme Dedecker ◽  
Florence Merlevède
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Hilbert Spaces ◽  
Conditional Central Limit Theorem

scholarly journals Asymptotic expansions in the conditional central limit theorem

1990 ◽  
Vol 63 (3) ◽  
pp. 273-292
Author(s):  
Dieter Landers ◽  
Lothar Rogge
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Asymptotic Expansions ◽  
Conditional Central Limit Theorem

CENTRAL LIMIT THEOREMS FOR SUPERLINEAR PROCESSES

2011 ◽  
Vol 11 (01) ◽  
pp. 71-80 ◽  
Author(s):  
DALIBOR VOLNÝ ◽  
MICHAEL WOODROOFE ◽  
OU ZHAO
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Limit Theorems ◽  
Sufficient Conditions ◽  
Distribution Functions ◽  
Causal Process ◽  
Linear Processes ◽  
Conditional Central Limit Theorem ◽  
The Central Limit Theorem

The Central Limit Theorem is studied for stationary sequences that are sums of countable collections of linear processes. Two sets of sufficient conditions are obtained. One restricts only the coefficients and is shown to be best possible among such conditions. The other involves an interplay between the coefficients and the distribution functions of the innovations and is shown to be necessary for the Conditional Central Limit Theorem in the case of a causal process with independent innovations.

RELATING TOP-DOWN WITH BOTTOM-UP APPROACHES IN THE EVALUATION OF ABS WITH LARGE COLLATERAL POOLS

2012 ◽  
Vol 15 (02) ◽  
pp. 1250011 ◽  
Author(s):  
NICOLAS DIENER ◽  
ROBERT JARROW ◽  
PHILIP PROTTER
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Cash Flow ◽  
Law Of Large Numbers ◽  
Credit Derivatives ◽  
Top Down ◽  
Bottom Up ◽  
Conditional Central Limit Theorem ◽  
Large Numbers

This paper uses a conditional law of large numbers and a conditional central limit theorem to provide simplified asymptotic valuation formulas for credit derivatives on baskets, including synthetic and cash-flow CDOs. In particular, approximate pricing procedures are provided for synthetic and cash-flow CDOs. In the process, this paper also clarifies the relation between the "top-down" and "bottom-up" approaches for pricing credit derivatives.

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