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Let {W{t),t ≥ 0} be a Brownian motion with drift coefficient μ and diffusion coefficient σ². We assume that the flow of a certain river can be modeled by the process {X(t),t ≥ 0} defined by

where k is a constant. Next, let d be a value of the flow above which the risk of flooding is high. Suppose that X(0) = d/3: Calculate the probability that the flow will reach the critical value d in the interval (0,1] if μ ≥ 0 and a - 1.

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Category:- Statistics and Probability
Reference No.:- M91887508

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