FIRST-PASSAGE TIME OF MARKOV PROCESSES TO MOVING BARRIERS HENRY C. TUCKWELL,* Monash University

نویسنده

  • FREDERIC Y. M. WAN
چکیده

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 of the process to the barrier. The procedure is first illustrated for first-passage-time problems where the solutions are known. The mean first-passage time of an Ornstein-Uhlenbeck process to an exponentially decaying barrier is then found by numerical solution of a partial differential equation. Extensions of the method to problems involving Markov processes with discontinuous sample paths and to cases where the process is confined between two moving barriers are also discussed. EXIT TIMES; DIFFUSION PROCESS; NEURAL FIRING; ORNSTEIN-UHLENBECK PROCESS

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Determination of the Very High Barriers to Conformational Processes by the Neat Racemization Technique. Part 1: Barriers to Ring Inversion in Dibenzo [a,c] Dinaphtho [2,3-e; 2,3-g] Cyclooctatetraene and Hindered Rotation in 2,2'-Dimethyl Binaphthyl

A method is described by which it is possible to determine the high barrier to ring inversion and hindered rotation by neat racemization of optically active compounds when the racemization is caused by ring inversion or hindered rotation. The method is based preparation of sufficiently pure enantiomers, mainly by chromatography on swollen microcrystalline triacetylcellulose (TAC). By this t...

متن کامل

On the effect of random perturbations in a nonlinear system

Many such studies have focused on first passage timesz3 or on steady state densities which have sometimes been estimated using electronic simulation.4 In some of the cases examined the noise has been multiplicative rather than additive and correlated (colored) rather than uncorrelated (white). Similar stochastic effects have been studied in several biological contexts5-’ In Ref. 3 the nonlinear...

متن کامل

On $L_1$-weak ergodicity of nonhomogeneous continuous-time Markov‎ ‎processes

‎In the present paper we investigate the $L_1$-weak ergodicity of‎ ‎nonhomogeneous continuous-time Markov processes with general state‎ ‎spaces‎. ‎We provide a necessary and sufficient condition for such‎ ‎processes to satisfy the $L_1$-weak ergodicity‎. ‎Moreover‎, ‎we apply‎ ‎the obtained results to establish $L_1$-weak ergodicity of quadratic‎ ‎stochastic processes‎.

متن کامل

Modified Maximum Likelihood Estimation in First-Order Autoregressive Moving Average Models with some Non-Normal Residuals

When modeling time series data using autoregressive-moving average processes, it is a common practice to presume that the residuals are normally distributed. However, sometimes we encounter non-normal residuals and asymmetry of data marginal distribution. Despite widespread use of pure autoregressive processes for modeling non-normal time series, the autoregressive-moving average models have le...

متن کامل

Aggregation and Numerical Techniques for Passage Time Calculations in Large semi-Markov Models

First-passage time densities and quantiles are important metrics in performance analysis. They are used in the analysis of mobile communication systems, web servers, manufacturing systems as well as for the analysis of the quality of service of hospitals and government organisations. In this report we look at computational techniques for the first-passage time analysis on highlevel models that ...

متن کامل

ذخیره 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 نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2001