On first exit times for homogeneous diffusion processes
نویسندگان
چکیده
Here t ≥ 0, wt is a standard d-dimensional Wiener process, coordinated as usual with some rightcontinuous non-decreasing flow of σ-algebras Ft ⊂ F ; fi and βi are nonrandom functions with respective values in R and R, (here and elsewhere i = 1, 2). The random vectors ai are measurable with respect to the σ-algebra F0 and ai ∈ Q̄ with probability 1(Q̄ denotes the closure of the region Q ). All vectors and matrices are real with Euclidean norm | · |. Consider the r.v.’s Ti = inf{t : yi(t) / ∈ Q}. These are the first exit times of the processes yi(t) from the region Q. Consider in Q the Dirichlet problem
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