TY - JOUR
T1 - On moments of Brownian functionals and their interpretation in terms of random walks
AU - Najnudel, Joseph
AU - Wu, Ching Tang
AU - Yen, Ju Yi
PY - 2020/6/1
Y1 - 2020/6/1
N2 - An identity in law, shown in Mansuy and Yor (2008); Yor (1991), involves integrals of quadratic functionals of the Brownian motion. The corresponding equalities of moments bring in equalities of multiple integrals of joint moments of the Brownian motion taken at different times. In the present paper, we compute these moments, and deduce an interpretation of some of these computations in terms of combinatorial sums indexed by different paths of random walks.
AB - An identity in law, shown in Mansuy and Yor (2008); Yor (1991), involves integrals of quadratic functionals of the Brownian motion. The corresponding equalities of moments bring in equalities of multiple integrals of joint moments of the Brownian motion taken at different times. In the present paper, we compute these moments, and deduce an interpretation of some of these computations in terms of combinatorial sums indexed by different paths of random walks.
KW - Brownian quadratic functionals
KW - Distributional integration by parts
UR - http://www.scopus.com/inward/record.url?scp=85079653807&partnerID=8YFLogxK
U2 - 10.1016/j.spl.2020.108724
DO - 10.1016/j.spl.2020.108724
M3 - Article (Academic Journal)
AN - SCOPUS:85079653807
VL - 161
JO - Statistics and Probability Letters
JF - Statistics and Probability Letters
SN - 0167-7152
M1 - 108724
ER -