Geodesic
Combinatorial methods for investigating the distribution of the trajectory amplitude of a random walk. II
Sbornik. Mathematics, Tome 21 (1973) no. 3, pp. 439-448 
V. K. Zakharov; O. V. Sarmanov. Combinatorial methods for investigating the distribution of the trajectory amplitude of a random walk. II. Sbornik. Mathematics, Tome 21 (1973) no. 3, pp. 439-448. http://geodesic.mathdoc.fr/item/SM_1973_21_3_a5/
@article{SM_1973_21_3_a5,
     author = {V. K. Zakharov and O. V. Sarmanov},
     title = {Combinatorial methods for investigating the distribution of the trajectory amplitude of a~random {walk.~II}},
     journal = {Sbornik. Mathematics},
     pages = {439--448},
     year = {1973},
     volume = {21},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1973_21_3_a5/}
}
TY  - JOUR
AU  - V. K. Zakharov
AU  - O. V. Sarmanov
TI  - Combinatorial methods for investigating the distribution of the trajectory amplitude of a random walk. II
JO  - Sbornik. Mathematics
PY  - 1973
SP  - 439
EP  - 448
VL  - 21
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/SM_1973_21_3_a5/
LA  - en
ID  - SM_1973_21_3_a5
ER  - 
%0 Journal Article
%A V. K. Zakharov
%A O. V. Sarmanov
%T Combinatorial methods for investigating the distribution of the trajectory amplitude of a random walk. II
%J Sbornik. Mathematics
%D 1973
%P 439-448
%V 21
%N 3
%U http://geodesic.mathdoc.fr/item/SM_1973_21_3_a5/
%G en
%F SM_1973_21_3_a5

Voir la notice de l'article provenant de la source Math-Net.Ru

For a Wiener process with a nonzero drift, the authors find the distribution density for the trajectory amplitude on a segment adjacent to the beginning of the trajectory. Formulas are given for the first two moments of the amplitude and it is shown that the change in the variance is monotonic. Bibliography: 2 titles.

[1] V. K. Zakharov, O. V. Sarmanov, “Kombinatornye metody issledovaniya raspredeleniya razmakha traektorii sluchainogo bluzhdaniya, I”, Matem. sb., 89 (131) (1972), 520–532 | Zbl

[2] W. Feller, “The asymptotic distribution of the range of sums of independent random variabiles”, Ann. Math. Stat., 22:3 (1951), 427–432 | DOI | MR | Zbl