Search results for " 60H35"

showing 3 items of 3 documents

Unbiased Inference for Discretely Observed Hidden Markov Model Diffusions

2021

We develop a Bayesian inference method for diffusions observed discretely and with noise, which is free of discretisation bias. Unlike existing unbiased inference methods, our method does not rely on exact simulation techniques. Instead, our method uses standard time-discretised approximations of diffusions, such as the Euler--Maruyama scheme. Our approach is based on particle marginal Metropolis--Hastings, a particle filter, randomised multilevel Monte Carlo, and importance sampling type correction of approximate Markov chain Monte Carlo. The resulting estimator leads to inference without a bias from the time-discretisation as the number of Markov chain iterations increases. We give conver…

FOS: Computer and information sciencesStatistics and ProbabilityDiscretizationComputer scienceMarkovin ketjutInference010103 numerical & computational mathematicssequential Monte CarloBayesian inferenceStatistics - Computation01 natural sciencesMethodology (stat.ME)010104 statistics & probabilitysymbols.namesakediffuusio (fysikaaliset ilmiöt)FOS: MathematicsDiscrete Mathematics and Combinatorics0101 mathematicsHidden Markov modelComputation (stat.CO)Statistics - Methodologymatematiikkabayesilainen menetelmäApplied MathematicsProbability (math.PR)diffusionmatemaattiset menetelmätMarkov chain Monte CarloMarkov chain Monte CarloMonte Carlo -menetelmätNoiseimportance sampling65C05 (primary) 60H35 65C35 65C40 (secondary)Modeling and Simulationsymbolsmatemaattiset mallitStatistics Probability and Uncertaintymultilevel Monte CarloParticle filterAlgorithmMathematics - ProbabilityImportance samplingSIAM/ASA Journal on Uncertainty Quantification
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Simulation of BSDEs with jumps by Wiener Chaos Expansion

2016

International audience; We present an algorithm to solve BSDEs with jumps based on Wiener Chaos Expansion and Picard's iterations. This paper extends the results given in Briand-Labart (2014) to the case of BSDEs with jumps. We get a forward scheme where the conditional expectations are easily computed thanks to chaos decomposition formulas. Concerning the error, we derive explicit bounds with respect to the number of chaos, the discretization time step and the number of Monte Carlo simulations. We also present numerical experiments. We obtain very encouraging results in terms of speed and accuracy.

Statistics and ProbabilityWiener Chaos expansionDiscretizationMonte Carlo methodTime stepConditional expectation01 natural sciences010104 statistics & probabilitybackward stochastic differential equations with jumpsFOS: MathematicsApplied mathematics60H10 60J75 60H35 65C05 65G99 60H070101 mathematicsMathematicsPolynomial chaosApplied MathematicsNumerical analysis010102 general mathematicsMathematical analysista111Probability (math.PR)numerical methodCHAOS (operating system)[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]Modeling and SimulationScheme (mathematics)Mathematics - Probability
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Random walk approximation of BSDEs with H{\"o}lder continuous terminal condition

2018

In this paper, we consider the random walk approximation of the solution of a Markovian BSDE whose terminal condition is a locally Hölder continuous function of the Brownian motion. We state the rate of the L2-convergence of the approximated solution to the true one. The proof relies in part on growth and smoothness properties of the solution u of the associated PDE. Here we improve existing results by showing some properties of the second derivative of u in space. peerReviewed

Statistics and Probabilitynumerical schemeHölder conditionSpace (mathematics)01 natural sciences010104 statistics & probabilityMathematics::Probability0101 mathematicsBrownian motionrandom walk approximationSecond derivativeMathematicsstokastiset prosessitSmoothness (probability theory)numeeriset menetelmät010102 general mathematicsMathematical analysisSpeed of convergenceBackward stochastic differential equationsFunction (mathematics)State (functional analysis)Random walk[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]random walk approxi-mationbackward stochastic differential equationsspeed of convergencespeed of convergence MSC codes : 65C30 60H35 60G50 65G99Mathematics - Probability
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