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Analytic solution and estimation of parameters on a stochastic exponential model for a technological diffusion process

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  • A. Katsamaki
  • C. H. Skiadas

Abstract

In this paper we examine the behaviour of a stochastic model that describes a technological diffusion process (continuously increasing process). Furthermore we obtain a solution for the proposed model through the estimation of the volatility using three different approximations. The adjustment of real data to the final stochastic model confirms its ability of describing and forecasting real cases.

Suggested Citation

  • A. Katsamaki & C. H. Skiadas, 1995. "Analytic solution and estimation of parameters on a stochastic exponential model for a technological diffusion process," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 11(1), pages 59-75, March.
    • Handle: RePEc:wly:apsmda:v:11:y:1995:i:1:p:59-75
    DOI: 10.1002/asm.3150110108
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    Citations

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    Cited by:

    1. C. H. Skiadas & A. N. Giovanis, 1997. "A stochastic Bass innovation diffusion model for studying the growth of electricity consumption in Greece," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 13(2), pages 85-101, June.
    2. Ahmed Nafidi & Meriem Bahij & Ramón Gutiérrez-Sánchez & Boujemâa Achchab, 2020. "Two-Parameter Stochastic Weibull Diffusion Model: Statistical Inference and Application to Real Modeling Example," Mathematics, MDPI, vol. 8(2), pages 1-11, January.
    3. Gutiérrez, R. & Nafidi, A. & Gutiérrez Sánchez, R., 2005. "Forecasting total natural-gas consumption in Spain by using the stochastic Gompertz innovation diffusion model," Applied Energy, Elsevier, vol. 80(2), pages 115-124, February.
    4. Ahmed Nafidi & Abdenbi El Azri & Ramón Gutiérrez-Sánchez, 2023. "A Stochastic Schumacher Diffusion Process: Probability Characteristics Computation and Statistical Analysis," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-15, June.
    5. Nafidi, A. & Bahij, M. & Achchab, B. & Gutiérrez-Sanchez, R., 2019. "The stochastic Weibull diffusion process: Computational aspects and simulation," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 575-587.
    6. Pramesti Getut, 2023. "Parameter least-squares estimation for time-inhomogeneous Ornstein–Uhlenbeck process," Monte Carlo Methods and Applications, De Gruyter, vol. 29(1), pages 1-32, March.
    7. Eva María Ramos-Ábalos & Ramón Gutiérrez-Sánchez & Ahmed Nafidi, 2020. "Powers of the Stochastic Gompertz and Lognormal Diffusion Processes, Statistical Inference and Simulation," Mathematics, MDPI, vol. 8(4), pages 1-13, April.
    8. Gutiérrez, R. & Gutiérrez-Sánchez, R. & Nafidi, A., 2009. "The trend of the total stock of the private car-petrol in Spain: Stochastic modelling using a new gamma diffusion process," Applied Energy, Elsevier, vol. 86(1), pages 18-24, January.
    9. R. Gutiérrez & R. Gutiérrez‐Sánchez & A. Nafidi, 2009. "Modelling and forecasting vehicle stocks using the trends of stochastic Gompertz diffusion models: The case of Spain," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(3), pages 385-405, May.
    10. Nafidi, Ahmed & El Azri, Abdenbi, 2021. "A stochastic diffusion process based on the Lundqvist–Korf growth: Computational aspects and simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 25-38.

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