The Stochastic Rayleigh diffusion model: Statistical inference and computational aspects. Applications to modelling of real cases

Applied Mathematics and Computation

Volumn 175, Issue 1, 2006, Pages 628-644

  Gutierrez R ^a   Gutierrez Sanchez R ^a   Nafidi, A ^a  

^a UNIVERSITY OF GRANADA   (Spain)

Author keywords

Computation of the estimation of drift parameters; Diffusion parameter; Kummer function; Life expectancy at birth; Simulation algorithm for stochastic differential equation; Stochastic Rayleigh diffusion model

Indexed keywords

COMPUTATIONAL METHODS; COMPUTER SIMULATION; COMPUTER SIMULATION LANGUAGES; DATA REDUCTION; DIFFERENTIAL EQUATIONS; DIFFUSION; PARAMETER ESTIMATION; PROBABILITY DENSITY FUNCTION; STATISTICAL METHODS;

BIOMETRY; KUMMER FUNCTIONS; LIFE EXPECTANCY AT BIRTH; SIMULATION ALGORITHM; STOCHASTIC RAYLEIGH DIFFUSION PROCESS; TREND FUNCTION;

RANDOM PROCESSES;

EID: 33644918622     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2005.07.047     Document Type: Article

References (31)

1. F. Black, and M. Scholes The pricing of options and corporate liabilities Political Economics 81 1973 637 659
2. M. Chesney, and J. Elliot Estimating the instantaneous volatility and covariance of risky assets Applied Stochastic Models and Data Analysis 11 1995 51 58
3. P. Clifford, and G. Wei The equivalence of the cox process with squared radial Ornstein-Uhlembeck intensity and the death process in a simple population model Annals of Applied Probability 3 3 1993 863 873
4. D. Cox Some statistical methods connected with series of events (with discussion) Journal of the Royal Statistical Society Series B 27 1955 129 164
5. J. Cox, Notes on option pricing i: constant elasticity of variance diffusions, Stanford University (1955).
6. Reprinted in Journal of Portfolio Management 1996;22:15-17.
7. J. Cox, and S. Ross The valuation of options for alternative stochastic processes Journal of Financial Economics 3 1976 145 166
8. D. Davidov, and V. Linetsky Pricing and hedging path-dependent options under cev processes Management Sciences 47 7 2001 949 965
9. L. Ferrante, S. Bompade, L. Possati, and L. Leone Parameter estimation in a Gompertzian stochastic-model for tumor growth Biometrics 56 2000 1076 1081
10. C. Gardiner Handbook of stochastic methods for physics chemistry and natural sciences second ed. 1990 Springer Verlag Berlin Germany
11. V. Giorno, A. Nobile, L. Ricciardi, and L. Sacerdote Some remarks on the Rayleigh process Journal of Applied Probability 23 1986 398 408
12. L. Gradshteyn, and I. Ryzhik Table of integrals, series and products 1979 Academic Press
13. M. Guerra, and L. Stefanini A comparative simulation study for estimating diffusion coefficient Mathematical and Computers in Simulation 53 2000 193 203
14. R. Gutiérrez, A. González, and F. Torres Estimation in multivariate lognormal diffusion process with exogenous factors Applied Statistics 4 1 1997 140 146
15. R. Gutiérrez, R. Gutiérrez-Sánchez, and A. Nafidi Stochastic Gompertz diffusion model statistical inference and applications Proceedings of the 17th Symposium on E.M.C.S.R. 2004 Austrian Society for Cybernetic Studies Vienna 146 150
16. R. Gutiérrez, A. Nafidi, and R. Gutiérrez-Sánchez Forecasting total natural-gas consumption in spain by using the stochastic gompertz innovation diffusion model Applied Energy 80 2 2005 115 124
17. R. Gutiérrez, A. Nafidi, R. Gutiérrez-Sánchez, P. Román, and F. Torres Inference in Gompertz type nonhomogeneous stochastic systems by means of discrete sampling Cybernetics and Systems 36 2005 203 216
18. R. Gutiérrez, L.M. Ricciardi, P. Román, and F. Torres First passage-time densities for time-non-homogeneous diffusion processes Journal of Applied Probability 34 3 1997 623 631
19. R. Gutiérrez, P. Román, and F. Torres A note on the volterra integral equation for the first-passage-time density Journal of Applied Probability 53 3 1995 635 648
20. R. Gutiérrez, P. Román, and F. Torres Inference and first-passage-time for the lognormal diffusion process with exogenous factors: application to modelling in economics Applied Stochastic Models in Business and Industry 15 4 1999 325 332
21. R. Gutiérrez, P. Román, and F. Torres Inference on some parametric functions in the univariate lognormal diffusion process with exogenous factors Test 10 2 2001 357 373
22. A. Katsamaki, and C. Skiadas Analytic solution and estimation of parameters on a stochastic exponential model for a technological diffusion process application Applied Stochastic Models and Data Analysis 11 1995 59 75
23. P. Kloeden, and E. Platen The numerical solution of stochastic differential equations 1992 Springer Berlin, Germany
24. P. Kloeden, E. Platen, H. Schurz, and M. Sorensen On effects of discretization on estimators of drift parameters for diffusion processes Journal of Applied Probability 33 1996 1061 1071
25. R. Merton Theory of rational options pricing Bell Journal of Economics and Management Science 4 1973 141 183
26. B. Prakasa Rao, Statistical inference for diffusion type process, Arnold (Ed.), 1999.
27. N. Rao, J. Borwankar, and D. Ramkrishma Numerical solution of Itô integral equations SIAM Journal of Control 12 1 1974 124 139
28. L. Rayleigh Philosophical Magazine Letters 32 1902 473
29. L. Ricciardi Diffusion processes and related topics in biology Lecture Notes in Biomathematics 1977 Springer Verlag Berlin Germany
30. J. Sepanier, and K. Oldham An Atlas of functions 1977 Springer Verlag Berlin, Germany
31. C. Skiadas, and A. Giovani A stochastic bass innovation diffusion model for studying the growth of electricity consumption in Greece Applied Stochastic Models and Data Analysis 13 1997 85 101