Journal ArticleDOI
Solutions for some diffusion processes with two barriers
Arnold L. Sweet,Jay C. Hardin +1 more
Reads0
Chats0
TLDR
In this article, a solution for the Wiener and Ornstein-Uhlenbeck (O.U.) processes in the presence of constant absorbing and/or reflecting barriers is obtained by means of separation of variables.Abstract:
Use is often made of the Wiener and Ornstein-Uhlenbeck (O.U.) processes in various applications of stochastic processes to problems of engineering interest. These applications frequently involve the presence of barriers. Although mathematical methods for solving Kolmogorov's forward equation for the above processes have previously been discussed ([1], [2]), many solutions for problems with two barriers do not seem to be available in the literature. Instead, one finds solutions for unrestricted processes or simulation used in place of analytical solutions in various applications ([3], [4], [5]). In this paper, solutions of Kolmogorov's forward equations in the presence of constant absorbing and/or reflecting barriers are obtained by means of separation of variables. This enables one to obtain expressions for the probability density functions for first passage times when absorbing barriers are present. The solution for the O.U. process is used to obtain a result of Breiman's [6] concerning first passage times.read more
Citations
More filters
Journal ArticleDOI
Detection of abrupt changes: theory and application
TL;DR: A unified framework for the design and the performance analysis of the algorithms for solving change detection problems and links with the analytical redundancy approach to fault detection in linear systems are established.
Journal ArticleDOI
Detection of Abrupt Changes: Theory and Applications.
Journal ArticleDOI
The Effect of Serial Correlation on the Performance of CUSUM Tests II
TL;DR: In this article, the authors employ the theory of weak convergence of cumulative sums to the Wiener Process to obtain large sample theory for cusum tests and study the effect of serial correlation on the performance of the one-sided cusUM test.
Journal ArticleDOI
Boundary-crossing probabilities for the Brownian motion and poisson processes and techniques for computing the power of the Kolmogorov-Smirnov test
TL;DR: In this paper, the first-passage distribution functions of a Brownian motion process are approximated by linear recursions whose coefficients are estimated by linearizing the boundaries within subintervals.
Journal ArticleDOI
Formulas for stopped diffusion processes with stopping times based on the maximum
TL;DR: In this article, the joint Laplace transform of time homogeneous diffusion processes and Brownian motion is derived, and the distribution of the maximum at $T$ is shown to be exponential for Brownian motions.
References
More filters
Journal ArticleDOI
Handbook of Mathematical Functions
Book
Conduction of Heat in Solids
H. S. Carslaw,John Conrad Jaeger +1 more
TL;DR: In this paper, a classic account describes the known exact solutions of problems of heat flow, with detailed discussion of all the most important boundary value problems, including boundary value maximization.
Book
The mathematics of diffusion
TL;DR: Though it incorporates much new material, this new edition preserves the general character of the book in providing a collection of solutions of the equations of diffusion and describing how these solutions may be obtained.