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- W4301793407 abstract "In this paper we consider the iterated Brownian motion $ ^{mu_1}_{mu_2}!I(t) = B_1^{mu_1} ( | B_{2}^{mu_2} (t)|) $ where $B_j^{mu_j} , j=1,2$ are two independent Brownian motions with drift $mu_j$. Here we study the last zero crossing of $ ^{mu_1}_{mu_2}!I(t) $ and for this purpose we derive the last zero-crossing distribution of the drifted Brownian motion. We derive also the joint distribution of the last zero crossing before $ t $ and of the first passage time through the zero level of a Brownian motion with drift $ mu $ after $ t $. All these results permit us to derive explicit formulas for ${^I_mu T_0} = sup { s < max_{0leq zleq t} |B_2(z)| : B_1^mu (s) = 0 }$. Also the iterated zero-crossing $ {^{mu_1} T}_{0, {^{mu_2} T}_{0,t}} $ is analyzed and extended to the case where the level of nesting is arbitrary." @default.
- W4301793407 created "2022-10-05" @default.
- W4301793407 creator A5039998868 @default.
- W4301793407 creator A5068607305 @default.
- W4301793407 date "2018-03-02" @default.
- W4301793407 modified "2023-09-26" @default.
- W4301793407 title "The last zero crossing of an iterated Brownian motion with drift" @default.
- W4301793407 doi "https://doi.org/10.48550/arxiv.1803.00877" @default.
- W4301793407 hasPublicationYear "2018" @default.
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