Statistical Inference for Ergodic Diffusion Processes

By Y. Kutoyants. 2004

495 citations recorded by the source corpus.

Subfields: Finance, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/46d54a6ddd9aed1a930a94742bd26caa08b9b826

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Citations in the corpus

Nonparametric estimation of diffusions: a differential equations approach (2012, background): “In particular, it is known (see for example Corollary 7.4 of Chung & Williams (1990) and Section 1.1.3 of Kutoyants (2004)) that for any Borel measurable and locally integrable function f on R we have for each t, Pα-a.s:∫ t 0 f(Xs)ds = ∫ ∞ −∞ Lt(u)f(u)du (4) where for every (t, x) Lt(x) = lim…”
Central limit theorems for additive functionals of ergodic Markov diffusions processes (2011, background): “Note that since we focus on an L2 framework, the natural normalization is the square root of the variance and we can only expect Gaussian fluctuations.”
Statistical aspects of the fractional stochastic calculus (2006, methodology): “We refer to the monographs [8], [36] or [22] for complete expositions of this topic.”
Penalized nonparametric mean square estimation of the coefficients of diffusion processes (2007, background): “Keywords: adaptive estimation; diffusion processes; discrete time observations; drift and diffusion coefficients; mean square estimator; model selection; penalized contrast; retrospective simulation”
Posterior consistency via precision operators for Bayesian nonparametric drift estimation in SDEs (2012, unknown): “…under study do not appear to be known, comparison with similar models suggests that the optimal rate for estimating a drift function b 0 that is β -regular (in Sobolev sense) may be T 1 2 in our setting (in a minimax sense over Sobolev balls for instance, cf. e.g. [22,35] for similar results).”
Parameter estimation for Ornstein-Uhlenbeck processes driven by α-stable Lévy motions (2007, methodology): “The trajectory fitting method was first proposed by Kutoyants [6] as a numerically attractive alternative to the well-developed maximum-likelihood estimators for continuous diffusion processes (see Dietz and Kutoyants [2], [3], Dietz [1], and Kutoyants [7]).”
Neural Networks with Cheap Differential Operators (2019, background): “A wide range of parameter estimation approaches have been proposed for SDEs (Prakasa Rao, 1999; Sørensen, 2004; Kutoyants, 2013).”
Drift estimation for a periodic mean reversion process (2010, background): “If the drift term given in (3) satisfies condition (5) then θ̂ML = Q −1 T PT .”
Polynomial type large deviation inequalities and quasi-likelihood analysis for stochastic differential equations (2011, background): “Kutoyants (2004) presented a polynomial-type large deviation inequality for onedimensional diffusions by means of the local time.”
Parameter Estimation for the Square-Root Diffusions: Ergodic and Nonergodic Cases (2012, background): “[18] This approach is rather theoretical, since the real data are discrete time observations.”
Parameter estimation for the stochastically perturbed Navier-Stokes equations (2010, background): “See the monographs [22], [25], and references therein for a comprehensive treatment.”
Parameter Estimation for Fractional Ornstein-Uhlenbeck Processes: Non-ergodic Case (2011, background): “If θ < 0 (ergodic case), the maximum likelihood estimator (MLE) of θ is asymptotically normal (see Liptser and Shiryaev [9], Kutoyants [8]).”