Computing the first passage time density of a time-dependent Ornstein-Uhlenbeck process to a moving boundary
نویسندگان
چکیده
In this paper we use the method of images to derive the closed-form formula for the first passage time density of a timedependent Ornstein–Uhlenbeck process to a parametric class of moving boundaries. The results are then applied to develop a simple, efficient and systematic approximation scheme to compute tight upper and lower bounds of the first passage time density through a fixed boundary. c © 2006 Elsevier Ltd. All rights reserved.
منابع مشابه
FIRST-PASSAGE TIME OF MARKOV PROCESSES TO MOVING BARRIERS HENRY C. TUCKWELL,* Monash University
The first-passage time of a Markov process to a moving barrier is considered as a first-exit time for a vector whose components include the process and the barrier. Thus when the barrier is itself a solution of a differential equation, the theory of first-exit times for multidimensional processes may be used to obtain differential equations for the moments and density of the first-passage time ...
متن کاملAPPLICATIONS OF THE REFLECTED ORNSTEIN-UHLENBECK PROCESS by
An Ornstein-Uhlenbeck process is the most basic mean-reversion model and has been used in various fields such as finance and biology. In some instances, reflecting boundary conditions are needed to restrict the state space of this process. We study an Ornstein-Uhlenbeck diffusion process with a reflecting boundary and its application to finance and neuroscience. In the financial application, th...
متن کاملFirst Passage Time Density for the Disease Progression of HIV Infected Patients
The time-dependent Ornstein-Uhlenbeck process (OU-process) is of immediate relevance to the progression of the CD4-cell counts of HIV infected patients. The first passage time density (FPTD) provides information about the disease level, and the predictions can then be used to optimize medical treatment. Despite the importance and wide applications of the time-dependent OU-process, no explicit a...
متن کاملReliability Analysis of Processes with Moving Cracked Material
The reliability of processes with moving elastic and isotropic material containing initial cracks is considered in terms of fracture. The material is modelled as a moving plate which is simply supported from two of its sides and subjected to homogeneous tension acting in the travelling direction. For tension, two models are studied: i) tension is constant with respect to time, and ii) tension v...
متن کاملThe Simulation and Approximation of the First Passage Time of the Ornstein-uhlenbeck Process of Neuron
JIANG, LIQIU. The Simulation and Approximation of the First Passage Time of the Ornstein–Uhlenbeck Process of Neuron. (Under the direction of Charles Eugene Smith.) Neurons communicate with each other via sequences of action potentials. The purpose of this study is to approximate the interval between action potentials which is also called the First Passage Time (FPT), the first time the membran...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Appl. Math. Lett.
دوره 19 شماره
صفحات -
تاریخ انتشار 2006