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Solving probability transform functional equations for numerical inversion

1992
*
Operations Research Letters
*

Many methods

doi:10.1016/0167-6377(92)90085-h
fatcat:fwnirsyfbnb35pci5uq7aifzra
*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. ...##
###
Numerical solution of fractional partial differential equations by numerical Laplace inversion technique

2013
*
Advances in Difference Equations
*

Then we use Stehfest's

doi:10.1186/1687-1847-2013-375
fatcat:np6ulb46djhnrbfg6uxt7a326y
*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. ...##
###
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 ...##
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Recovery of Foreign Interest Rates from Exchange Binary Options

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 ...

##
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Computational Probabilistic Analysis and Transformation Method in the Earth Remote Research

2020
*
E3S Web of Conferences
*

A

doi:10.1051/e3sconf/202022302001
fatcat:wyl7abwhqfcudbzgdt5ze5uo44
*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 ...##
###
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

1998
*
European Physical Journal B : Condensed Matter Physics
*

This integral

doi:10.1007/s100510050484
fatcat:sly33ifj3vfu5ch6tx4q33y6dy
*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 ...##
###
Probabilistic Scaling for the Numerical Inversion of Nonprobability Transforms

1997
*
INFORMS journal on computing
*

Subject classifications: Mathematics,

doi:10.1287/ijoc.9.2.175
fatcat:3wpnfgullzcqlibbf3obp2obti
*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. ...##
###
Determining the Volatility in Option Pricing From Degenerate Parabolic Equation

2022
*
WSEAS Transactions on Mathematics
*

This contribution deals with the

doi:10.37394/23206.2022.21.73
fatcat:apjkeotfdjfirfspkwr6yk5lki
*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 ...##
###
Valuation of European Call Option via Inverse Fourier Transform

2017
*
Information Technology and Management Science
*

The Fast Fourier

doi:10.1515/itms-2017-0016
fatcat:2rsnep4o7zckdet5dtf4mvhytq
*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 ...##
###
A Comprehensive Method for Solving Finite-State Semi-Markov Processes
[article]

2021
*
arXiv
*
pre-print

Semi-Markov processes (SMPs) provide a rich framework

arXiv:1212.1440v3
fatcat:wnagrkt5dfgkrkbdqa2o7y5wii
*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*. . ." ...##
###
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

2002
*
Proceedings of the 2002 ACM SIGMETRICS international conference on Measurement and modeling of computer systems - SIGMETRICS '02
*

Corresponding theoretical results

doi:10.1145/511344.511345
fatcat:hzhmq2t6k5abxbd6xavp4a5sau
*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*...##
###
Passage time distributions in large Markov chains

2002
*
Proceedings of the 2002 ACM SIGMETRICS international conference on Measurement and modeling of computer systems - SIGMETRICS '02
*

Corresponding theoretical results

doi:10.1145/511334.511345
dblp:conf/sigmetrics/HarrisonK02
fatcat:3gpydizwszap7cuqulvnva64yu
*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*...##
###
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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