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- Type of Document: M.Sc. Thesis
- Language: Farsi
- Document No: 42953 (02)
- University: Sharif University of Technology
- Department: Mathematics Sciences
- Advisor(s): Zohuri Zangeneh, Bijan
- Abstract:
- Theoretical investigation of stochastic delay differential equation driven by fractional Brownian motion is important issue because of its application in the modeling. In this thesis, after defining of the stochastic integral with respect to fractional Brownian motion and describing the delay differential equation, we prove existence and
uniqueness of solution of stochastic delay differential equation driven by fractional Brownian motion with Hurst parameter H>1/2 and we show that the solution has finite moments from each order. Moreover we show when the delay goes to zero, thesolutions to these equations converge, almost surely and in Lp, to the solution for the equation without delay. The stochastic integral with respect to the fractional
Brownian motion is a pathwise Reiman-Stieltjes integral - Keywords:
- Fractional Brownian Motion ; Delay Differential Equations ; Riemann-Stiltjes Integral
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