function Y = FTsymexp(X,sigma2)
% Fourier transform of the symetric exponential
% with variance sigma2
if nargin<2, sigma2=1; end;
Y = 1./(1+sigma2*X.^2/2);
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% This is part of the package EstimHidden devoted to the estimation of
%
% 1/ the density of X in a convolution model where Z=X+noise1 is observed
%
% 2/ the functions b (drift) and s^2 (volatility) in an "errors in variables"
% model where Z and Y are observed and assumed to follow:
% Z=X+noise1 and Y=b(X)+s(X)*noise2.
%
% 3/ the functions b (drift) and s^2 (volatility) in an stochastic
% volatility model where Z is observed and follows:
% Z=X+noise1 and X_{i+1} = b(X_i) + s(X_i)*noise2
%
% in any cases the density of noise1 is known. We consider three cases for
% this density : Gaussian ('normal'), Laplace ('symexp') and log(Chi2)
% ('logchi2)
%
% See function DeconvEstimate.m and examples in files ExampleDensity.m and
% ExampleRegression.m
%
% Authors : F. COMTE and Y. ROZENHOLC
%
%
% For more information, see the following references:
%
% DENSITY DECONVOLUTION
%%%%%%%%%%%%%%%%%%%%%%%
%
% 1/ "Penalized contrast estimator for density deconvolution",
% The Canadian Journal of Statistics, 34, 431-452, 2006.
% b y F . C O M T E , Y . R O Z E N H O L C , and M . - L . T A U P I N
%
% 2/ "Finite sample penalization in adaptive density deconvolution",
% Journal of Statistical Computation and Simulation.
% Available online.
% b y F . C O M T E , Y . R O Z E N H O L C , and M . - L . T A U P I N
%
% 3/ "Adaptive density estimation for general ARCH models",
% Preprint HAL-CNRS : hal-00101417 at http://hal.archives-ouvertes.fr/
% b y F . C O M T E , J. DEDECKER, and M . - L . T A U P I N .
%
% REGRESSION and AUTO-REGRESSION
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% 4/ "Nonparametric estimation of the regression function in an
% errors-in-variables model",
% Statistica Sinica, 17, n3, 1065-1090, 2007.
% b y F . C O M T E and M . - L . T A U P I N
%
% 5/ "Adaptive estimation of the dynamics of a discrete time stochastic
% volatility model",
% Preprint HAL-CNRS : hal-00170740 at http://hal.archives-ouvertes.fr/
% by F . C O M T E, C. LACOUR, and Y. R O Z E N H O L C .
%
%
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%
% Y o u c a n u s e t h i s s o f t w a r e f o r N O N - C O M M E R C I A L U S E O N L Y .
%
% Y o u c a n d i s t r i b u t e t h i s s o f w a r e u n c h a n g e d a n d o n l y u n c h a n g e d , w h i c h i m p l i e s
% i n c l u d i n g a l l f i l e s f o u n d i n t h e f o l d e r c o i n t a i n n i n g t h i s f i l e .
%
% T h i s s o f t w a r e , a n d a n y p a r t o f i t , i s p r o p o s e d f o r N O N - C O M M E R C I A L U S E
% O N L Y .
%
% P l e a s e , c o n t a c t t h e a u t h o r f o r a n d b e f o r e a n y n o n - a c a d e m i c u s e
% o f t h i s s o f t w a r e .
%
% T o r e p r o d u c e t h i s c o d e o r a n y p a r t o f t h i s c o d e i n t h e o r i g i n a l l a n g u a g e
% o r i n a n y o t h e r l a n g u a g e , f o r c o m m e r c i a l u s e , p l e a s e c o n t a c t t h e A u t h o r
%
% F o r a c a d e m i c p u r p o s e , c i t e this package and t h e c o n n e c t e d p a p e r s .
%
% C o r r e s p o n d i n g a u t h o r : Y . R o z e n h o l c , y v e s . r o z e n h o l c @ u n i v - p a r i s 5 . f r
%
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%
% Examples in files ExampleDensity.m and ExampleRegression.m
%
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