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Exact Solutions of Stochastic Differential Equations: Gompertz, Generalized Logistic and Revised Exponential

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  • Christos H. Skiadas

    (Technical University of Crete)

Abstract

Exact analytic solutions of some stochastic differential equations are given along with characteristic futures of these models as the Mean and Variance. The procedure is based on the Ito calculus and a brief description is given. Classical stochastic models and also new models are provided along with a related bibliography. Stochastic models included are the Gompertz, Linear models with multiplicative noise term, the Revised Exponential and the Generalized Logistic. Emphasis is given in the presentation of stochastic models with a sigmoid form for the mean value. These models are of particular interest when dealing with the innovation diffusion into a specific population, including the spread of epidemics, diffusion of information and new product adoption.

Suggested Citation

  • Christos H. Skiadas, 2010. "Exact Solutions of Stochastic Differential Equations: Gompertz, Generalized Logistic and Revised Exponential," Methodology and Computing in Applied Probability, Springer, vol. 12(2), pages 261-270, June.
    • Handle: RePEc:spr:metcap:v:12:y:2010:i:2:d:10.1007_s11009-009-9145-3
    DOI: 10.1007/s11009-009-9145-3
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    References listed on IDEAS

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    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.
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    Cited by:

    1. Fabien Campillo & Marc Joannides & Irène Larramendy-Valverde, 2016. "Analysis and Approximation of a Stochastic Growth Model with Extinction," Methodology and Computing in Applied Probability, Springer, vol. 18(2), pages 499-515, June.
    2. M’hamed Gaïgi & Idris Kharroubi & Thomas Lim, 2020. "Optimal Exploitation of a General Renewable Natural Resource under State and Delay Constraints," Mathematics, MDPI, vol. 8(11), pages 1-25, November.
    3. Virginia Giorno & Amelia G. Nobile, 2019. "Restricted Gompertz-Type Diffusion Processes with Periodic Regulation Functions," Mathematics, MDPI, vol. 7(6), pages 1-19, June.
    4. Karim, Md Aktar Ul & Aithal, Vikram & Bhowmick, Amiya Ranjan, 2023. "Random variation in model parameters: A comprehensive review of stochastic logistic growth equation," Ecological Modelling, Elsevier, vol. 484(C).

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