컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0498 |
|---|---|
| 분류(Section) | Poster Session |
| 분과(Session) | Probability / Stochastic Process / Statistics (SS-12) |
| 영문제목 (Title(Eng.)) |
An application of the LTDRM in parameter estimation of one-dimensional It\^o processes |
| 저자(Author(s)) |
Piriya Prunglerdbuathong1, Khamron Mekchay1, Sanae Rujivan2 Chulalongkorn University, Bangkok, Thailand1, Walailak University, Nakhon Si Thammarat, Thailand2 |
| 초록본문(Abstract) | An It\^o process is a stochastic process commonly used for modeling time evolution of dynamic systems in many fields. In order to estimate the unknown parameters of an It\^o process based on the maximum likelihood method, the transitional probability density function (PDF) of the It\^o process is needed. In fact, the transitional PDF is the solution of a Fokker-Planck equation subject to an initial condition in which the transitional PDF is set to be coincided with the Dirac delta function at the initial time. In this research, we applied the numerical method called the Laplace transform dual reciprocity method (LTDRM) to approximate the solution of the Fokker-Planck equations, corresponding to a one-dimensional It\^o process. The highlight of the LTDRM for solving this type of problems is to transform the Dirac delta function into the Laplace space and then use the dual reciprocity method (DRM) to solve the transformed equation without approximating the Dirac delta function after that use the numerical inverse Laplace transform which is Stehfest\rq{}s algorithm to convert the solutions in the Laplace space into the transitional PDF of a one-dimensional It\^o process in the real space. The result of this research is the transitional PDF of a one-dimensional It\^o process in order to estimate parameters further. |
| 분류기호 (MSC number(s)) |
60H35 |
| 키워드(Keyword(s)) | It\^o process, Fokker-Planck equation, transitional probability density function, LTDRM, maximum likelihood estimate |
| 강연 형태 (Language of Session (Talk)) |
English |