SDE based Generalized Innovation Diffusion Modeling
Diffusion models are rigorously implemented in marketing research to predict the actual trend of innovations over time. These models can be classified in terms of deterministic and stochastic behavior. Deterministic models ignore the randomness in the adoption rate of an innovation that occurs due t...
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International Journal of Mathematical, Engineering and Management Sciences
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doaj-6a2bd8baad5b45d789ae608bb7a9bd182020-11-25T02:19:08ZengInternational Journal of Mathematical, Engineering and Management SciencesInternational Journal of Mathematical, Engineering and Management Sciences2455-77492455-77492019-06-014369770710.33889/IJMEMS.2019.4.3-055SDE based Generalized Innovation Diffusion ModelingShakshi Singhal0Adarsh Anand1Ompal Singh2Department of Operational Research, University of Delhi, Delhi-110007, IndiaDepartment of Operational Research, University of Delhi, Delhi-110007, IndiaDepartment of Operational Research, University of Delhi, Delhi-110007, IndiaDiffusion models are rigorously implemented in marketing research to predict the actual trend of innovations over time. These models can be classified in terms of deterministic and stochastic behavior. Deterministic models ignore the randomness in the adoption rate of an innovation that occurs due to environmental and internal system disturbances. Therefore, in the present research, a generalized stochastic diffusion model using Itô’s process is proposed that jointly study the product awareness and eventual adoption of an innovation. Convolution function is applied to integrate these two processes. In addition, different probability distributions are employed, which are relevant for describing the product awareness and adoption processes. Non-linear regression is further carried out to validate the proposed models and parameters are estimated based on the actual sales data from Smartphone and automobile industries. The forecasting results indicate that the proposed models perform empirically better than the already established diffusion models.https://www.ijmems.in/assets/55-ijmems-ror13-vol.-4%2c-no.-3%2c-697%E2%80%93707%2c-2019.pdfAwarenessConvolutionItô’s integralStochastic differential equationTechnology diffusion |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Shakshi Singhal Adarsh Anand Ompal Singh |
spellingShingle |
Shakshi Singhal Adarsh Anand Ompal Singh SDE based Generalized Innovation Diffusion Modeling International Journal of Mathematical, Engineering and Management Sciences Awareness Convolution Itô’s integral Stochastic differential equation Technology diffusion |
author_facet |
Shakshi Singhal Adarsh Anand Ompal Singh |
author_sort |
Shakshi Singhal |
title |
SDE based Generalized Innovation Diffusion Modeling |
title_short |
SDE based Generalized Innovation Diffusion Modeling |
title_full |
SDE based Generalized Innovation Diffusion Modeling |
title_fullStr |
SDE based Generalized Innovation Diffusion Modeling |
title_full_unstemmed |
SDE based Generalized Innovation Diffusion Modeling |
title_sort |
sde based generalized innovation diffusion modeling |
publisher |
International Journal of Mathematical, Engineering and Management Sciences |
series |
International Journal of Mathematical, Engineering and Management Sciences |
issn |
2455-7749 2455-7749 |
publishDate |
2019-06-01 |
description |
Diffusion models are rigorously implemented in marketing research to predict the actual trend of innovations over time. These models can be classified in terms of deterministic and stochastic behavior. Deterministic models ignore the randomness in the adoption rate of an innovation that occurs due to environmental and internal system disturbances. Therefore, in the present research, a generalized stochastic diffusion model using Itô’s process is proposed that jointly study the product awareness and eventual adoption of an innovation. Convolution function is applied to integrate these two processes. In addition, different probability distributions are employed, which are relevant for describing the product awareness and adoption processes. Non-linear regression is further carried out to validate the proposed models and parameters are estimated based on the actual sales data from Smartphone and automobile industries. The forecasting results indicate that the proposed models perform empirically better than the already established diffusion models. |
topic |
Awareness Convolution Itô’s integral Stochastic differential equation Technology diffusion |
url |
https://www.ijmems.in/assets/55-ijmems-ror13-vol.-4%2c-no.-3%2c-697%E2%80%93707%2c-2019.pdf |
work_keys_str_mv |
AT shakshisinghal sdebasedgeneralizedinnovationdiffusionmodeling AT adarshanand sdebasedgeneralizedinnovationdiffusionmodeling AT ompalsingh sdebasedgeneralizedinnovationdiffusionmodeling |
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1724878243335503872 |