Multisource Bayesian sequential hypothesis testing

On some probability space (Ω,F,P), let (X)t≥0, 1 ≤ i ≤ d be d independent Brownian motions with constant drifts μ(i), 1 ≤ i ≤ d, and (T (j) n , Z n )n≥1, 1 ≤ j ≤ m be m independent compound Poisson processes independent of the Brownian motions (X)t≥0, 1 ≤ i ≤ d. For every 1 ≤ j ≤ m, (T (j) n )n≥1 are the arrival times, and (Z n )n≥1 are the marks on some measurable space (E, E), with arrival rates λ(j) and mark distributions ν(j)(·) on (E, E). Suppose that μ(i), 1 ≤ i ≤ d and (λ(j), ν)1≤j≤m are unknown, but exactly one of the following two simple hypotheses,