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math.PR2023
Explicit formula of boundary crossing probabilities for continuous local martingales to constant boundary
Yoann Potiron
An explicit formula for the probability that a continuous local martingale crosses a one or two-sided random constant boundary in a finite time interval is derived. We obtain that…
math.PR2023
Non-explicit formula of boundary crossing probabilities by the Girsanov theorem
Yoann Potiron
This paper derives several formulae for the probability that a Wiener process, which has a stochastic drift and random variance, crosses a one-sided stochastic boundary within a fi…
math.PR2021
Approximation convergence in the inverse first-passage time problem
Yoann Potiron
The inverse first-passage time problem determines a boundary such that the first-passage time of a Wiener process to this boundary has a given distribution. An approximation which…