# Boundary noncrossings of additive Wiener fields

### Details

Download: BIB_CD06405DABD4.P001.pdf (117.69 [Ko])

State: Serval

Version: author

State: Serval

Version: author

Serval ID

serval:BIB_CD06405DABD4

Type

**Article**: article from journal or magazin.

Collection

Publications

Fund

Title

Boundary noncrossings of additive Wiener fields

Journal

Lithuanian Mathematical Journal

ISSN

0363-1672 (Print)

1573-8825 (Online)

1573-8825 (Online)

Publication state

Published

Issued date

2014

Peer-reviewed

Oui

Volume

54

Number

3

Pages

277-289

Language

english

Abstract

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.

Keywords

Boundary noncrossing probability, Reproducing kernel Hilbert space, Additive Wiener field, Polar cones, Logarithmic asymptotics, Brownian sheet, Brownian pillow

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Create date

09/07/2014 23:07

Last modification date

03/03/2018 20:29