2 results
A prediction problem of the branching random walk
- Part of
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- Journal:
- Journal of Applied Probability / Volume 41 / Issue A / 2004
- Published online by Cambridge University Press:
- 14 July 2016, pp. 25-31
- Print publication:
- 2004
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The joint density of the maximum and its location for a Wiener process with drift
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- Journal:
- Journal of Applied Probability / Volume 16 / Issue 2 / June 1979
- Published online by Cambridge University Press:
- 14 July 2016, pp. 423-427
- Print publication:
- June 1979
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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,
; (c) the endpoint 
, 
, 
