Journal article

Crossing probabilities for diffusion processes with piecewise continuous boundaries

Wang L, Pötzelberger K ...see all

Methodology and Computing in Applied Probability, vol. 9, issue 1 (2007) pp. 21-40

  • 8


    Mendeley users who have this article in their library.
  • 23


    Citations of this article.
Sign in to save reference


We propose an approach to compute the boundary crossing probabilities for a class of diffusion processes which can be expressed as piecewise monotone (not necessarily one-to-one) functionals of a standard Brownian motion. This class includes many interesting processes in real applications, e.g., Ornstein-Uhlenbeck, growth processes and geometric Brownian motion with time dependent drift. This method applies to both one-sided and two-sided general nonlinear boundaries, which may be discontinuous. Using this approach explicit formulas for boundary crossing probabilities for certain nonlinear boundaries are obtained, which are useful in evaluation and comparison of various omputational algorithms. Moreover, numerical computation can be easily done by Monte Carlo integration and the approximation errors for general boundaries are automatically calculated. Some numerical examples are presented.

Author-supplied keywords

  • Boundary crossing probabilities
  • Brownian motion
  • Diffusion process
  • First hitting time
  • First passage time
  • Wiener process

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document

Get full text


  • Liqun Wang

  • Klaus Pötzelberger

Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free