Search results for "Girsanov theorem"

showing 3 items of 3 documents

Transportation cost inequalities on path and loop groups

2005

AbstractLet G be a connected Lie group with the Lie algebra G. The action of Cameron–Martin space H(G) on the path space Pe(G) introduced by L. Gross (Illinois J. Math. 36 (1992) 447) is free. Using this fact, we define the H-distance on Pe(G), which enables us to establish a transportation cost inequality on Pe(G). This method will be generalized to the path space over the loop group Le(G), so that we obtain a transportation cost inequality for heat measures on Le(G).

Discrete mathematicsPath (topology)Adjoint representationLie groupGirsanov theoremSpace (mathematics)Action (physics)Heat measuresLoop groupsLoop (topology)Loop groupLie algebraWasserstein distanceAnalysisMathematicsH-distanceJournal of Functional Analysis
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Exact simulation of first exit times for one-dimensional diffusion processes

2019

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 …

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]
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A Path-Integral Approach to the Cameron-Martin-Maruyama-Girsanov Formula Associated to a Bilaplacian

2012

We define the Wiener product on a bosonic Connes space associated to a Bilaplacian and we introduce formal Wiener chaos on the path space. We consider the vacuum distribution on the bosonic Connes space and show that it is related to the heat semigroup associated to the Bilaplacian. We deduce a Cameron-Martin quasi-invariance formula for the heat semigroup associated to the Bilaplacian by using some convenient coherent vector. This paper enters under the Hida-Streit approach of path integral.

Pure mathematicsGirsanov theoremArticle SubjectSemigroupMathematics::Operator Algebraslcsh:MathematicsSpace (mathematics)lcsh:QA1-939AlgebraDistribution (mathematics)Product (mathematics)Path integral formulationPath spaceAnalysisMathematicsJournal of Function Spaces and Applications
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