ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

12. Probability and Statistics

1991 MS Classification: 60 Borodin, Andrei, St. Petersburg Department Steklov Mathematical Institute, Russia Distributions of functionals of a particular non-Markov process Let w(s), s ≥ 0, be the Brownian motion process,

ℓ(t, x) = lim_{ε↓0} \frac{1}{ε} ∫_{0}^{t} 1_{[x,x+ε)}(w(s)) ds, t ≥ 0, x ∈ R^{1},

be its local time. For arbitrary fixed α_{k}, r_{k} ∈ R^{1}, k = 1, 2, …, m, the non-Markov process

ξ(s) = w(s) + ∑_{k=1}^{m} α_{k}ℓ(s, r_{k}),

is considered. The talk deals with the method of calculation of distributions of integral functionals, infimum and supremum functionals, and local times of the process ξ(s). This method is based on the solution of a family differential problems depending on the varying gluing conditions. Some examples of applications are considered.