Nonparametric Bayesian volatility estimation for gamma-driven stochastic differential equations
Artikel i vetenskaplig tidskrift, 2022
We study a nonparametric Bayesian approach to estimation of the volatility function of a stochastic differential equation driven by a gamma process. The volatility function is modelled a priori as piecewise constant, and we specify a gamma prior on its values. This leads to a straightforward procedure for posterior inference via an MCMC procedure. We give theoretical performance guarantees (minimax optimal contraction rates for the posterior) for the Bayesian estimate in terms of the regularity of the unknown volatility function. We illustrate the method on synthetic and real data examples.
nonparametric Bayesian estimation
Gamma process
stochastic differential equation
Författare
Denis Belomestny
Universität Duisburg-Essen
National Research University Higher School of Economics
Shota Gugushvili
Wageningen University and Research
Moritz Schauer
Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik
Peter Spreij
Korteweg-de Vries Institute for Mathematics
Radboud Universiteit
Bernoulli
1350-7265 (ISSN)
Vol. 28 4 2151-2180Ämneskategorier
Beräkningsmatematik
Sannolikhetsteori och statistik
Matematisk analys
DOI
10.3150/21-BEJ1413