6533b852fe1ef96bd12aa338
RESEARCH PRODUCT
Exact simulation of first exit times for one-dimensional diffusion processes
Cristina ZuccaSamuel Herrmannsubject
Girsanov theoremand phrases: Exit timeDiscretizationsecondary: 65N75Exit time Brownian motion diffusion processes Girsanov’s transformation rejection sampling exact simulation randomized algorithm conditioned Brownian motion.MSC 65C05 65N75 60G40Exit time01 natural sciencesGirsanov’s transformationrandomized algorithm010104 statistics & probabilityrejection samplingGirsanov's transformationexact simulationFOS: MathematicsApplied mathematicsMathematics - Numerical Analysis0101 mathematicsConvergent seriesBrownian motion60G40MathematicsNumerical AnalysisApplied MathematicsMathematical financeRejection samplingProbability (math.PR)diffusion processesNumerical Analysis (math.NA)conditioned Brownian motionRandomized algorithm010101 applied mathematics[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]Computational MathematicsModeling and Simulationconditioned Brownian motion 2010 AMS subject classifications: primary 65C05Brownian motionRandom variableMathematics - ProbabilityAnalysis[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]description
International audience; The simulation of exit times for diffusion processes is a challenging task since it concerns many applications in different fields like mathematical finance, neuroscience, reliability horizontal ellipsis The usual procedure is to use discretization schemes which unfortunately introduce some error in the target distribution. Our aim is to present a new algorithm which simulates exactly the exit time for one-dimensional diffusions. This acceptance-rejection algorithm requires to simulate exactly the exit time of the Brownian motion on one side and the Brownian position at a given time, constrained not to have exit before, on the other side. Crucial tools in this study are the Girsanov transformation, the convergent series method for the simulation of random variables and the classical rejection sampling. The efficiency of the method is described through theoretical results and numerical examples.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2019-05-10 |