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A variance reduction method for parametrized stochastic differential equations using the reduced basis paradigm
- Source :
- Communications in Mathematical Sciences, Communications in Mathematical Sciences, 2010, 8 (3), pp.735-762. ⟨10.4310/CMS.2010.v8.n3.a7⟩, Communications in Mathematical Sciences, International Press, 2010, 8 (3), pp.735-762. ⟨10.4310/CMS.2010.v8.n3.a7⟩, Commun. Math. Sci. 8, no. 3 (2010), 735-762
- Publication Year :
- 2010
- Publisher :
- International Press of Boston, 2010.
-
Abstract
- International audience; In this work, we develop a reduced-basis approach for the efficient computation of parametrized expected values, for a large number of parameter values, using the control variate method to reduce the variance. Two algorithms are proposed to compute online, through a cheap reduced-basis approximation, the control variates for the computation of a large number of expectations of a functional of a parametrized Ito stochastic process (solution to a parametrized stochastic differential equation). For each algorithm, a reduced basis of control variates is pre-computed offline, following a so-called greedy procedure, which minimizes the variance among a trial sample of the output parametrized expectations. Numerical results in situations relevant to practical applications (calibration of volatility in option pricing, and parameter-driven evolution of a vector field following a Langevin equation from kinetic theory) illustrate the efficiency of the method.
- Subjects :
- 65C05
Mathematical optimization
General Mathematics
010103 numerical & computational mathematics
Expected value
Control variates
Variance Reduction
01 natural sciences
Stochastic differential equation
Reduced-Basis Methods
60H10, 65C05
FOS: Mathematics
Mathematics - Numerical Analysis
0101 mathematics
Mathematics
60H10
Basis (linear algebra)
Stochastic process
Applied Mathematics
Numerical Analysis (math.NA)
010101 applied mathematics
Stochastic partial differential equation
Langevin equation
Stochastic Differential Equations
Variance reduction
[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Subjects
Details
- ISSN :
- 19450796 and 15396746
- Volume :
- 8
- Database :
- OpenAIRE
- Journal :
- Communications in Mathematical Sciences
- Accession number :
- edsair.doi.dedup.....c834eef2601928952a94c3c8a4fd54a3