Discrete Stochastic Integration

Authors

  • Bushra Suliman

Abstract

We present in this article a game of chance (Saint Petersburg Paradox) and generalize it on a probability space as an example of a previsible (predictable) process, from which we get a discrete stochastic integration (DSI). Then we define a martingale  and present it as a good integrator of a discrete stochastic integration , which is called the martingale transform of  by  such that  is a previsible process.

After that we present the most important properties of the DSI, which include that the DSI is also a martingale , the theorem of stability for it, the definition of the covariation of two given martingales and the proof that the DSI is centered with a specific given variance.

Finally, we define Doob-decomposition and the quadratic variation and present Itȏ-formula as a certain sort of it.

 

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Published

2018-10-01

How to Cite

1.
Suliman B. Discrete Stochastic Integration. TUJ-BA [Internet]. 2018Oct.1 [cited 2024Apr.27];39(6). Available from: https://journal.tishreen.edu.sy/index.php/bassnc/article/view/4028

Issue

Vol. 39 No. 6 (2017): العلوم الاساسية

Section

Articles

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