Chulalongkorn University Theses and Dissertations (Chula ETD)
Half-normal approximation for Number of returns to origin of random walks
Other Title (Parallel Title in Other Language of ETD)
การประมาณค่าแบบกึ่งปกติสำหรับจำนวนครั้งที่กลับมายังจุดเริ่มต้นของแนวเดินแบบสุ่ม
Year (A.D.)
2016
Document Type
Thesis
First Advisor
Kritsana Neammanee
Faculty/College
Faculty of Science (คณะวิทยาศาสตร์)
Degree Name
Master of Science
Degree Level
Master's Degree
Degree Discipline
Mathematics
DOI
10.58837/CHULA.THE.2016.1687
Abstract
Let (Xn) be a sequence of independent identically distributed random variables with P(X₁=1) = p, P(X₁ = -1) for 0 < p < 1. A random walk is a discrete time stochastic process (Sn) defined by S₀=0 and [Equation] for n ≥1. Kn is called the number of returns to the origin if [Equation] and [Equation]. In case of symmetric random walk, i.e., [Equation] | D bler (2015) showed that the distribution of Kn can be approximated by half-normal distribution and he also gave a uniform bound of this approximation. After that Sama-ae et.al. (2016) gave non-uniform bounds. In this thesis, we improve a non-uniform bound of Sama-ae et.al. In case of asymmetric random walk, i.e., [Equation], we give a distribution of Kn and show that it is not convergent to half-normal distribution
Other Abstract (Other language abstract of ETD)
ให้ (Xn) เป็นลำดับของตัวแปรสุ่มที่เป็นอิสระต่อกันและมีการแจกแจงแบบเดียวกัน โดยที่ P(X₁=1) = p, P(X₁ = -1) เมื่อ 0
Creative Commons License
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Recommended Citation
Siripraparat, Tatpon, "Half-normal approximation for Number of returns to origin of random walks" (2016). Chulalongkorn University Theses and Dissertations (Chula ETD). 63136.
https://digital.car.chula.ac.th/chulaetd/63136