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Data-Based Analysis and Reconstruction of Stochastic Jump-Diffusion Processes Using Statistical Moments (With Applications to Bacteria Trapped in Optical Tweezers and Stock Markets)

Amir Hossein Naseri Golestani | 2024

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 57173 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Rahimi Tabar, Mohammad Reza; Seyedreihani, Nader
  7. Abstract:
  8. Derivation of the dynamic stochastic equation based on experimental data to describe the behavior of the system has a wide application in various branches of natural sciences, social sciences, medical sciences and treatment, economics and financial markets, and so on. For this purpose, it is necessary to calculate the coefficients of the Kramers-Moyal equation from the data. The two common methods in statistical analysis and data mathematics for the numerical calculation of the coefficients of the Kramers-Moyal equation are the histogram method and the kernel method, each of which has limitations; including that they can be used in one and at most two dimensions. In this research, we present a more accurate method based on the calculation of statistical moments and overcoming the previous problems. In this method, in addition to better analysis and more accurate formulation than what has previously been done, we also examine the jumps in the system data. Furthermore, we investigate the influence of the behavior of each dimension of the system on other dimensions and determine the interactions among the dimensions of the system. Then, as examples of the application of this method, we analyze the equations related to the behavior of bacteria trapped in optical tweezers. The analysis of stock market prices and the impact of the dominant stock on the market on other existing stocks will also be another example in this research
  9. Keywords:
  10. Kramers-Moyal Coefficient ; Statistical Moment Equations ; Jump-Diffusion Model ; Langevin Equation ; Stochastic Process ; Optical Tweezer ; Stock Market

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