serval:BIB_CD06405DABD4
Boundary noncrossings of additive Wiener fields
10.1007/s10986-014-9243-y
000340400100003
Hashorva
E.
author
Mishura
Y.
author
article
2014
Lithuanian Mathematical Journal
0363-1672
1573-8825
journal
54
3
277-289
Let {W (i) (t), t a a"e(+)}, i = 1, 2, be two Wiener processes, and let W (3) = {W (3)(t), t a a"e (+) (2) } be a two-parameter Brownian sheet, all three processes being mutually independent. We derive upper and lower bounds for the boundary noncrossing probability P (f) = P{W (1)(t (1)) + W (2)(t (2)) + W (3)(t) + f(t) a parts per thousand currency sign u(t), t a a"e (+) (2) }, where f, u : a"e (+) (2) -> a"e are two general measurable functions. We further show that, for large trend functions gamma f > 0, asymptotically, as gamma -> a, P (gamma f) is equivalent to , where is the projection of f onto some closed convex set of the reproducing kernel Hilbert space of the field W(t) = W (1)(t (1)) + W (2)(t (2)) + W (3)(t). It turns out that our approach is also applicable for the additive Brownian pillow.
Boundary noncrossing probability
Reproducing kernel Hilbert space
Additive Wiener field
Polar cones
Logarithmic asymptotics
Brownian sheet
Brownian pillow
eng
60_published
peer-reviewed
University of Lausanne
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