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18
The Incomplete Gamma Functions Since Tricomi
 In Tricomi's Ideas and Contemporary Applied Mathematics, Atti dei Convegni Lincei, n. 147, Accademia Nazionale dei Lincei
, 1998
"... The theory of the incomplete gamma functions, as part of the theory of conuent hypergeometric functions, has received its rst systematic exposition by Tricomi in the early 1950s. His own contributions, as well as further advances made thereafter, are surveyed here with particular emphasis on asy ..."
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Cited by 15 (1 self)
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The theory of the incomplete gamma functions, as part of the theory of conuent hypergeometric functions, has received its rst systematic exposition by Tricomi in the early 1950s. His own contributions, as well as further advances made thereafter, are surveyed here with particular emphasis on asymptotic expansions, zeros, inequalities, computational methods, and applications.
Best choice from the planar Poisson process
 Stoch. Proc. Appl
, 2004
"... Various bestchoice problems related to the planar homogeneous Poisson process in finite or semiinfinite rectangle are studied. The analysis is largely based on properties of the onedimensional boxarea process associated with the sequence of records. We prove a series of distributional identities ..."
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Cited by 6 (1 self)
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Various bestchoice problems related to the planar homogeneous Poisson process in finite or semiinfinite rectangle are studied. The analysis is largely based on properties of the onedimensional boxarea process associated with the sequence of records. We prove a series of distributional identities involving exponential and uniform random variables, and resolve the PetruccelliPorosinskiSamuels paradox on coincidence of asymptotic values in certain discretetime optimal stopping problems. 1
A coherent approach to noninteger order derivatives
 SIGNAL PROCESSING, SPECIAL ISSUE ON FRACTIONAL CALCULUS AND APPLICATIONS
, 2006
"... The relation showing that the GrünwaldLetnikov and generalised Cauchy derivatives are equal is presented. This establishes a bridge between two different formulations and simultaneously between the classic integer order derivatives and the fractional ones. Starting from the generalised Cauchy deriv ..."
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Cited by 4 (1 self)
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The relation showing that the GrünwaldLetnikov and generalised Cauchy derivatives are equal is presented. This establishes a bridge between two different formulations and simultaneously between the classic integer order derivatives and the fractional ones. Starting from the generalised Cauchy derivative formula, new relations are obtained, namely a regularised version that makes the concept of pseudofunction appear naturally without the need for a rejection of any infinite part. From the regularised derivative, new formulations are deduced and specialised first for the real functions and afterwards for functions with Laplace transforms obtaining the definitions proposed by Liouville. With these tools suitable definitions of fractional linear systems are obtained.
The estimation of Laplace random vectors in additive white Gaussian noise
 IEEE TRANS. ON SIG. PROC
, 2008
"... This paper develops and compares the maximum a posteriori (MAP) and minimum meansquare error (MMSE) estimators for spherically contoured multivariate Laplace random vectors in additive white Gaussian noise. The MMSE estimator is expressed in closedform using the generalized incomplete gamma funct ..."
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Cited by 3 (0 self)
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This paper develops and compares the maximum a posteriori (MAP) and minimum meansquare error (MMSE) estimators for spherically contoured multivariate Laplace random vectors in additive white Gaussian noise. The MMSE estimator is expressed in closedform using the generalized incomplete gamma function. We also find a computationally efficient yet accurate approximation for the MMSE estimator. In addition, this paper develops an expression for the MSE for any estimator of spherically contoured multivariate Laplace random vectors in additive white Gaussian noise (AWGN), the development of which again depends on the generalized incomplete gamma function. The estimators are motivated and tested on the problem of waveletbased image denoising.
Transformation of the extended gamma function Γ 2,0 0,2 [(B,X)] with applications to astrophysical thermonuclear functions
 Astrophysics and Space Science
, 1999
"... Two representations of the extended gamma functions Γ 2,0 0,2 [(b,x)] are proved. These representations are exploited to find a transformation relation between two Fox’s Hfunctions. These results are used to solve Fox’s Hfunction in terms of Meijer’s Gfunction for certain values of the parameters ..."
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Cited by 2 (1 self)
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Two representations of the extended gamma functions Γ 2,0 0,2 [(b,x)] are proved. These representations are exploited to find a transformation relation between two Fox’s Hfunctions. These results are used to solve Fox’s Hfunction in terms of Meijer’s Gfunction for certain values of the parameters. A closed form representation of the kernel of the Bessel type integral transform is also proved. 1.
Robust replication of volatility derivatives
, 2003
"... Postscript/PDF files of these overheads can be downloaded from: www.petercarr.net or www.math.nyu.edu\research\carrp\papers ..."
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Cited by 2 (1 self)
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Postscript/PDF files of these overheads can be downloaded from: www.petercarr.net or www.math.nyu.edu\research\carrp\papers
EXTENSION OF THERMONUCLEAR FUNCTIONS THROUGH THE PATHWAY MODEL INCLUDING MAXWELLBOLTZMANN AND TSALLIS DISTRIBUTIONS
, 708
"... Abstract. The MaxwellBoltzmannian approach to nuclear reaction rate theory is extended to cover Tsallis statistics (Tsallis, 1988) and more general cases of distribution functions. An analytical study of respective thermonuclear functions is being conducted with the help of statistical techniques. ..."
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Abstract. The MaxwellBoltzmannian approach to nuclear reaction rate theory is extended to cover Tsallis statistics (Tsallis, 1988) and more general cases of distribution functions. An analytical study of respective thermonuclear functions is being conducted with the help of statistical techniques. The pathway model, recently introduced by Mathai (2005), is utilized for thermonuclear functions and closedform representations are obtained in terms of Hfunctions and Gfunctions. MaxwellBoltzmannian thermonuclear functions become particular cases of the extended thermonuclear functions. A brief review on the development of the theory of analytic representations of nuclear reaction rates is given. 1
REVIEW OF MATHEMATICAL TECHNIQUES APPLICABLE IN ASTROPHYSICAL REACTION RATE THEORY
, 2002
"... Abstract. An overview is presented on statistical techniques for the analytic evaluation of integrals for nonresonant, nonresonant depleted, nonresonant cutoff, nonresonant sccreened, and resonant thermonuclear reaction rates. The techniques are based on statistical distribution theory and the ..."
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Abstract. An overview is presented on statistical techniques for the analytic evaluation of integrals for nonresonant, nonresonant depleted, nonresonant cutoff, nonresonant sccreened, and resonant thermonuclear reaction rates. The techniques are based on statistical distribution theory and the theory of Meijer’s Gfunction and Fox’s Hfunction. The implementation of Meijer’s Gfunction in Mathematica constituts an additional utility for analytic manipulations and numerical computation of thermonuclear reaction rate integrals. Recent results in the astrophysical literature related to the use of analytic thermonuclear reaction rates are incorporated. 1 1
Bayesian Estimation of Bessel K Form Random Vectors in AWGN
"... Abstract—We present new Bayesian estimators for sphericallycontoured Bessel K form (BKF) random vectors in additive white Gaussian noise (AWGN). The derivations are an extension of existing results for the scalar BKF and multivariate Laplace (MLAP) densities. MAP and MMSE estimators are derived. We ..."
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Abstract—We present new Bayesian estimators for sphericallycontoured Bessel K form (BKF) random vectors in additive white Gaussian noise (AWGN). The derivations are an extension of existing results for the scalar BKF and multivariate Laplace (MLAP) densities. MAP and MMSE estimators are derived. We show that the MMSE estimator can be written in exact form in terms of the generalized incomplete Gamma function. Computationally efficient approximations are given. We compare the proposed exact and approximate MMSE estimators with recent results using the BKF density, both in terms of the shrinkage rules and the associated meansquare error. Index Terms—Bayesian estimation, Bessel K form density, MAP estimator, MMSE estimator, wavelet denoising.