On the geometric Brownian motion with state-dependent variable exponent diffusion term
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914104762957824 |
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| author | Avci, Mustafa |
| author_facet | Avci, Mustafa |
| contents | We propose a new stochastic model involving state-dependent variable exponent $p(\cdot)$ which allows modeling of systems where noise intensity adapts to the current state. This new flexible theoretical framework generalizes both the geometric Brownian motion (GBM) and the Constant-Elasticity-of-Variance (CEV) models. We prove an existence-uniqueness theorem. We obtain an upper-bound approximation for the model-to-model pathwise error between our model and the GBM model as well as test its accuracy through analytical and numerical error estimates. A detailed comparison of the Itô and Stratonovich interpretations for the proposed model is presented in the Appendix. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_07130 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the geometric Brownian motion with state-dependent variable exponent diffusion term Avci, Mustafa Analysis of PDEs Probability 60G07, 60H15, 60H20, 60H30 We propose a new stochastic model involving state-dependent variable exponent $p(\cdot)$ which allows modeling of systems where noise intensity adapts to the current state. This new flexible theoretical framework generalizes both the geometric Brownian motion (GBM) and the Constant-Elasticity-of-Variance (CEV) models. We prove an existence-uniqueness theorem. We obtain an upper-bound approximation for the model-to-model pathwise error between our model and the GBM model as well as test its accuracy through analytical and numerical error estimates. A detailed comparison of the Itô and Stratonovich interpretations for the proposed model is presented in the Appendix. |
| title | On the geometric Brownian motion with state-dependent variable exponent diffusion term |
| topic | Analysis of PDEs Probability 60G07, 60H15, 60H20, 60H30 |
| url | https://arxiv.org/abs/2508.07130 |