Introduction to Stochastic Differential Equations

Kostrista, Entela and Çibuku, Denajda (2018) Introduction to Stochastic Differential Equations. Journal of Natural Sciences and Mathematics of UT, 3 (5-6). pp. 189-195. ISSN 2671-3039

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Stochastic differential equations provide a link between probability theory and ordinary and partial differential equations. The stochastic modeler benefits from centuries of development of the physical sciences, and many classic results of mathematics can be given new intuitive interpretations. There are several reasons why one should learn more about SDE: They have a wide range of applications outside mathematics, there are many fruitful connections to other mathematical disciplines and the subject has a rapidly developing life of its own as a fascinating research field with many interesting unanswered questions. The paper is meant to be an appetizer and is the answer of the issues: In what situations does the SDE arise? What are its essential features? What are the applications and the connections to other fields? First we have constructed Wiener process, or Brownian motion. The study of Brownian motion can be intense, but the main ideas are a simple definition and the application of Ito ̂ Lemma. Then we will deal with the stochastic calculus and then we will show that SDEs can be solved. In the end we will see the modeling problems: How does SDEs model the physical situation and white noise process which is the generalized mean-square derivative of the Wiener process or Brownian motion. Keywords: SDE, Brownian motion, Ito ̂’s formula, white noise

Item Type: Article
Subjects: Q Science > Q Science (General)
Divisions: Faculty of Engineering, Science and Mathematics > School of Electronics and Computer Science
Depositing User: Unnamed user with email
Date Deposited: 05 Jun 2019 08:34
Last Modified: 05 Jun 2019 08:34

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