The joint density of the maximum and its location for a Wiener process with drift
- 1 June 1979
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 16 (02) , 423-427
- https://doi.org/10.1017/s0021900200046623
Abstract
We give a simple expression for the joint probability density of: (a) the maximum value Y = max [X(t), 0 ≦ t ≦ T); (b) its location ; (c) the endpoint X(T), where X(t) = Xc (t) is a Wiener process with drift, Xc (t) = W(t) + ct, 0 ≦ t ≦ T. That is, we find the density p(θ, y, x) = p(θ, y, x; c, T) of , Y, X(T), p(θ, y, x; , Xc (T) ∈ dx) is given by, 0 < θ < T, x ≦ y, 0 < y,Keywords
This publication has 2 references indexed in Scilit:
- Radon-Nikodym Derivatives of Gaussian MeasuresThe Annals of Mathematical Statistics, 1966
- Transformations of Weiner Integrals Under TranslationsAnnals of Mathematics, 1944