TRANSFORMATION ON DIFFUSION PROCESSES AND FIRST PASSAGE TIME TO THE MOVING BOUNDARIES

Authors : Salih ÇELEBIOĞLU, Tahir KHANIYEV, Cihan AKSOP, Salih ÇELEBİOĞLU, Tahir KHANİYEV

Pages : 57-62

View : 18 | Download : 12

Publication Date : 2013-03-31

Article Type : Other Papers

Abstract :Normal 0 21 false false false TR X-NONE X-NONE MicrosoftInternetExplorer4 /* Style Definitions */ table.MsoNormalTable {mso-style-name:`Normal Tablo`; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-qformat:yes; mso-style-parent:``; mso-padding-alt:0cm 5.4pt 0cm 5.4pt; mso-para-margin-top:0cm; mso-para-margin-right:0cm; mso-para-margin-bottom:10.0pt; mso-para-margin-left:0cm; line-height:115%; mso-pagination:widow-orphan; font-size:11.0pt; font-family:`Calibri`,`sans-serif`; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:`Times New Roman`; mso-fareast-theme-font:minor-fareast; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:`Times New Roman`; mso-bidi-theme-font:minor-bidi;} In this paper, we study the first passage time of a diffusion process to a moving boundary. Under some special conditions we apply a transformation to diffusion process and to the boundary function and then in each case obtain the first passage time distribution of the original process by the first passage time distribution of transformed process to transformed boundary. In addition, by applying these transformations to the Ornstein- Uhlenbeck and Wiener processes the first passage time distributions for the new boundaries are presented as examples.   Keywords: Diffusion process; Ornstein-Uhlenbeck process; First passage times; Moving boundaries; Lambert function; Hyperbolic function; Fixed boundaries
Keywords : Diffusion process, Ornstein Uhlenbeck process, First passage times, Moving boundaries, Lambert function, Hyperbolic function, Fixed boundaries