Boundary crossing probability for Brownian motion

By Klaus Pötzelberger, Liqun Wang. Journal of Applied Probability, 2001

121 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/f68f3350d338f60adfc5e8e5e33f58c0ad1f632e

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In Statistics and Probability

Citations in the corpus

Confidence bands for Brownian motion and applications to Monte Carlo simulation (2007, methodology): “Using this result, Potzelberger and Wang (2001) derive the following Monte Carlo estimator of P1(u) P̂1(u)n,N = 1 N N ∑”
A class of Lévy process models with almost exact calibration to both barrier and vanilla FX options (2010, unknown): “If we wish to price, for example, a DNT option with barrier levels at L and U (with continuously monitored barriers), we can use results in Potzelberger and Wang (2001) concerning the probability of a Brownian bridge process hitting either of the barrier levels.”
On the exact and ε-strong simulation of (jump) diffusions (2013, background): “In this section, we briefly outline results pertaining to the probability that a Brownian bridge sample path is contained within a particular interval [2,32] (Theorem 3) and how to simulate events of this probability [6] (Corollary 3).”
EXPLICIT BOUNDS FOR APPROXIMATION RATES OF BOUNDARY CROSSING PROBABILITIES FOR THE WIENER PROCESS (2005, methodology): “A popular choice for f± is piecewise-linear boundaries, for which a combination of the total probability formula, the Markov property, and explicit formulae for linear boundary crossing probabilities for the Brownian bridge process immediately gives the desired probability P(f−, f+) as a finite-dime”
A Factorisation of Diffusion Measure and Finite Sample Path Constructions (2008, background): “This probability has a known expression in terms of an infinite series, a result which can be traced back to Doob (1949), although see Pötzelberger and Wang (2001) for a more recent reference.”