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Intrinsic expansions for averaged diffusion processes
- Source :
- Stochastic Processes and their Applications. 127:2560-2585
- Publication Year :
- 2017
- Publisher :
- Elsevier BV, 2017.
-
Abstract
- We show that the rate of convergence of asymptotic expansions for solutions of SDEs is generally higher in the case of degenerate (or partial) diffusion compared to the elliptic case, i.e. it is higher when the Brownian motion directly acts only on some components of the diffusion. In the scalar case, this phenomenon was already observed in (Gobet and Miri 2014) using Malliavin calculus techniques. In this paper, we provide a general and detailed analysis by employing the recent study of intrinsic functional spaces related to hypoelliptic Kolmogorov operators in (Pagliarani et al. 2016). Relevant applications to finance are discussed, in particular in the study of path-dependent derivatives (e.g. Asian options) and in models incorporating dependence on past information.
- Subjects :
- Averaged diffusion
Statistics and Probability
Hypoelliptic Kolmogorov operators
Scalar (mathematics)
Asymptotic expansion
Malliavin calculus
01 natural sciences
Asian option
Mathematics - Analysis of PDEs
0502 economics and business
FOS: Mathematics
Statistical physics
0101 mathematics
Brownian motion
Hypoelliptic Kolmogorov operator
Mathematics
050208 finance
Applied Mathematics
Probability (math.PR)
010102 general mathematics
05 social sciences
Probability and statistics
Rate of convergence
Modeling and Simulation
Hypoelliptic operator
Mathematics - Probability
Analysis of PDEs (math.AP)
Subjects
Details
- ISSN :
- 03044149
- Volume :
- 127
- Database :
- OpenAIRE
- Journal :
- Stochastic Processes and their Applications
- Accession number :
- edsair.doi.dedup.....96d4be0133352620f919ad0722678bce