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Solving probability transform functional equations for numerical inversion

Joseph Abate, Ward Whitt
1992 Operations Research Letters  
Many methods for numerically inverting transforms require values of the transform at complex arguments.  ...  However, in some applications, the transforms are only characterized implicitly via functional equations. This is illustrated by the busy-period distribution in the M/G/1 queue.  ...  We thank Bharat Doshi and Dave Lucantoni for helpful discussions.  ... 
doi:10.1016/0167-6377(92)90085-h fatcat:fwnirsyfbnb35pci5uq7aifzra

Numerical solution of fractional partial differential equations by numerical Laplace inversion technique

Mohammad Javidi, Bashir Ahmad
2013 Advances in Difference Equations  
Then we use Stehfest's numerical algorithm for calculating inverse Laplace transform to retrieve the time domain solution.  ...  In this paper, we propose a numerical method for solving fractional partial differential equations. This method is based on the homotopy perturbation method and Laplace transform.  ...  Acknowledgements The authors thank the reviewers for their constructive remarks that led to the improvement of the original manuscript.  ... 
doi:10.1186/1687-1847-2013-375 fatcat:np6ulb46djhnrbfg6uxt7a326y

Page 7793 of Mathematical Reviews Vol. , Issue 97M [page]

1997 Mathematical Reviews  
(I-MILAN; Milan) Numerical methods for solving a hyperbolic inverse integro-differential problem. (English summary) J. Inverse Ill-Posed Probl. 4 (1996), no. 6, 535—552.  ...  the free term (for the integral equation), and the probability densities used in the construction of stochastic estimates.” 65T Numerical methods in Fourier analysis 97m:65249 65R30 45L05 65520 Schréter  ... 

Recovery of Foreign Interest Rates from Exchange Binary Options

M. Mitsuhiro, Y. Ota
2015 Computer Technology and Application  
For space-dependent real drift, we obtain stable linearization and an integral equation.  ...  For example, the numerical method in Section 5 for solving an inverse problem is in effective.  ...  Since the Laplace transform of the convolution is the product of Laplace transforms of convoluted functions, we have Numerical Example In this section, we propose and numerically test our algorithm  ... 
doi:10.17265/1934-7332/2015.02.004 fatcat:yvdh53fboreevfnlgxslsvyxru

Computational Probabilistic Analysis and Transformation Method in the Earth Remote Research

Boris Dobronets, Olga Popova, Alexey Merko, G.M. Tsybulski Gennady, M.V. Noskov, Yu.A. Maglinets
2020 E3S Web of Conferences  
A numerical example of the joint probability density function of the vector of a solution of a system of nonlinear equations with random input data is given.  ...  The article deals with the issues of numerical modeling of problems with random input data. Finding the joint probability density function of the vector of output parameters is considered.  ...  Equation (3) states that the joint probability density function for the random vector X is the joint probability density function for the random vector Z at the corresponding point, but it is recalculated  ... 
doi:10.1051/e3sconf/202022302001 fatcat:wyl7abwhqfcudbzgdt5ze5uo44

Page 4451 of Mathematical Reviews Vol. , Issue 82j [page]

1982 Mathematical Reviews  
The authors describe an algorithm for the numerical inversion of the Mellin transform by using Laguerre polynomials.  ...  Then, by substituting T=(1/27)cot(@/2), in the Mellin transform of gy(r), an algorithm for the numerical inversion of the Mellin transform is obtained.  ... 

On the probability distributions of relaxation times in glasses

H. Keiter, M. Rosenberg
1998 European Physical Journal B : Condensed Matter Physics  
This integral equation is solved by a Mellin or a Stieltjes transform. Beyond known results, we obtain the probability distribution of the Havriliak-Negami dielectric function.  ...  They may serve as checks for numerical procedures applied to the underlying ill-posed problem, if experimental data for the dielectric function are used.  ...  For the inverse Mellin transform or the inverse (two-side) Laplace transform to our knowledge only the principal application of a stabilizing function is known, but explicit conditions for it do not seem  ... 
doi:10.1007/s100510050484 fatcat:sly33ifj3vfu5ch6tx4q33y6dy

Probabilistic Scaling for the Numerical Inversion of Nonprobability Transforms

Gagan L. Choudhury, Ward Whitt
1997 INFORMS journal on computing  
Subject classifications: Mathematics, functions: scaling for numerical transform inversion. Queues, algorithms: scaling for numerical transform inversion.  ...  It is known that probability density functions and probability mass functions can usually be calculated quite easily by numerically inverting their transforms (Laplace transforms and generating functions  ...  Calculating these non-probability functions by numerical inversion has proved to be substantially more difficult than calculating probability distributions.  ... 
doi:10.1287/ijoc.9.2.175 fatcat:3wpnfgullzcqlibbf3obp2obti

Determining the Volatility in Option Pricing From Degenerate Parabolic Equation

Yilihamujiang Yimamu
2022 WSEAS Transactions on Mathematics  
This contribution deals with the inverse volatility problem for a degenerate parabolic equation from numerical perspective.  ...  principal term coefficient problem for classical parabolic equation into the inverse source problem for degenerate parabolic equation in bounded region.  ...  We apply the linearization method and variable substitutions to transform the inverse principal term coefficient problem for classical parabolic equation into the inverse source problem for a degenerate  ... 
doi:10.37394/23206.2022.21.73 fatcat:apjkeotfdjfirfspkwr6yk5lki

Valuation of European Call Option via Inverse Fourier Transform

Oskars Rubenis, Andrejs Matvejevs
2017 Information Technology and Management Science  
The Fast Fourier transform based on trapezoidal quadrature is numerically unstable if a standard cumulative probability function is used.  ...  Characteristic function corresponds to Normal Inverse Gaussian (NIG) probability density function.  ...  The equation for pricing European call option using inverse Fourier transformation operator: exp η ψ , ; η . ( 13 ) The equation for pricing European call option where Fourier transformation operator is  ... 
doi:10.1515/itms-2017-0016 fatcat:2rsnep4o7zckdet5dtf4mvhytq

A Comprehensive Method for Solving Finite-State Semi-Markov Processes [article]

Richard L. Warr, David H. Collins
2021 arXiv   pre-print
Semi-Markov processes (SMPs) provide a rich framework for many real-world problems. However, due to difficulty implementing practical solutions they are rarely used with their full capability.  ...  With the exception of some of the simplest cases, solutions to SMPs are inherently numerical, and SMPs have been underutilized by practitioners because of difficulty implementing the theory in applications  ...  , it is well known that this inverse transform is not stable numerically . . ."  ... 
arXiv:1212.1440v3 fatcat:wnagrkt5dfgkrkbdqa2o7y5wii

Page 4091 of Mathematical Reviews Vol. , Issue 94g [page]

1994 Mathematical Reviews  
We present mathematical and numerical analyses of the time-to-frequency DFT of the complex exponential function and of the frequency-to-time inverse DFT of the relaxation func- tion.  ...  They also provide a brief review of the literature on the optimization of nonadaptive direct 65U Numerical methods in probability and statistics 94g:65149 methods for integral equations with regular kernels  ... 

Passage time distributions in large Markov chains

Peter G. Harrison, William J. Knottenbelt
2002 Proceedings of the 2002 ACM SIGMETRICS international conference on Measurement and modeling of computer systems - SIGMETRICS '02  
Corresponding theoretical results for semi-Markov chains are also presented.  ...  Probability distributions of response times are important in the design and analysis of transaction processing systems and computercommunication systems.  ...  ACKNOWLEDGEMENTS The authors would like to thank their M.Sc. student Teresa Au-Young for bringing the Laguerre method to their attention in her M.Sc. thesis "Numerical Techniques for Laplace Transform  ... 
doi:10.1145/511344.511345 fatcat:hzhmq2t6k5abxbd6xavp4a5sau

Passage time distributions in large Markov chains

Peter G. Harrison, William J. Knottenbelt
2002 Proceedings of the 2002 ACM SIGMETRICS international conference on Measurement and modeling of computer systems - SIGMETRICS '02  
Corresponding theoretical results for semi-Markov chains are also presented.  ...  Probability distributions of response times are important in the design and analysis of transaction processing systems and computercommunication systems.  ...  ACKNOWLEDGEMENTS The authors would like to thank their M.Sc. student Teresa Au-Young for bringing the Laguerre method to their attention in her M.Sc. thesis "Numerical Techniques for Laplace Transform  ... 
doi:10.1145/511334.511345 dblp:conf/sigmetrics/HarrisonK02 fatcat:3gpydizwszap7cuqulvnva64yu

Page 3843 of Mathematical Reviews Vol. , Issue 98F [page]

1998 Mathematical Reviews  
Summary: “It is known that probability density functions and probability mass functions usually can be calculated quite easily by numerically inverting their transforms (Laplace transforms and generating  ...  In this article we propose a simple new scaling procedure for nonprobability functions that is based on transforming the given function into a probability density function or a probability mass function  ... 
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