Mathematics MS Thesis Defense by Neslihan Şahin

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KOÇ UNIVERSITY

GRADUATE SCHOOL OF SCIENCES & ENGINEERING

MATHEMATICS

MS THESIS DEFENSE BY NESLIHAN SAHIN

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Title: Weak Solutions of Stochastic Differential Equations and One-Sided Sticky Brownian Motion

Speaker: Neslihan Şahin

Time: July 17, 2017, 14:30

Place: Room Eng 208

Koç University

Rumeli Feneri Yolu

Sariyer, Istanbul

Thesis Committee Members:

Assoc. Prof. Mine Çağlar (Advisor, Koc University)

Assoc. Prof. Atilla Yılmaz (Koc University)

Assoc. Prof. Semih Onur Sezer (Sabancı University)

Abstract:

One-sided sticky Brownian motion is a slowly reflecting Brownian motion because it spends positive amount of time at zero before reflection. The primary purpose of this thesis is to analyze the stochastic differential equation or the equivalent system which has one-sided sticky Brownian motion as a weak solution. The work of H. J. Engelbert and G. Peskir entitled  “Stochastic Differential Equations for Sticky Brownian Motion” published in Stochastics in 2012 is taken into consideration. They study the stochastic differential equation for one-sided sticky Brownian motion by first analyzing the stochastic differential system for two-sided sticky Brownian motion and then using these results for the one-sided system. In this thesis, one-sided version is analyzed without the use of the results for the two-sided version, but with the help of the relation between one-sided and two-sided sticky Brownian motion. The proofs for two-sided sticky Brownian motion given in [Engelbert and Peskir, 2012] paper are followed. We prove the stochastic differential equation, or the equivalent system, admits a weak solution but does not have a strong solution.