## Journal of Applied Probability

### Boundary crossing probability for Brownian motion

#### Abstract

Wang and Pötzelberger (1997) derived an explicit formula for the probability that a Brownian motion crosses a one-sided piecewise linear boundary and used this formula to approximate the boundary crossing probability for general nonlinear boundaries. The present paper gives a sharper asymptotic upper bound of the approximation error for the formula, and generalizes the results to two-sided boundaries. Numerical computations are easily carried out using the Monte Carlo simulation method. A rule is proposed for choosing optimal nodes for the approximating piecewise linear boundaries, so that the corresponding approximation errors of boundary crossing probabilities converge to zero at a rate of O(1/n2).

#### Article information

Source
J. Appl. Probab. Volume 38, Number 1 (2001), 152-164.

Dates
First available: 5 August 2001

http://projecteuclid.org/euclid.jap/996986650

Digital Object Identifier
doi:10.1239/jap/996986650

Mathematical Reviews number (MathSciNet)
MR1816120

Zentralblatt MATH identifier
0986.60079

#### Citation

Pötzelberger, Klaus; Wang, Liqun. Boundary crossing probability for Brownian motion. Journal of Applied Probability 38 (2001), no. 1, 152--164. doi:10.1239/jap/996986650. http://projecteuclid.org/euclid.jap/996986650.