Statistics of Random Processes Ii: Applications

By Robert Sh. Liptser, A. Shiryayev. 2000

444 citations recorded by the source corpus.

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Citations in the corpus

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]).”
Ornstein–Uhlenbeck Processes and Extensions (2009, methodology): “…models based on hypothetical continuous time observation of a process over a finite interval, and the testing of hypotheses about them, for example, in a likelihood framework (Liptser and Shiryaev (1978), Basawa and Prakasa Rao (1980), Heyde (1997), Kutoyants (2004)), which provide much insight.”
A filtering approach to tracking volatility from prices observed at random times (2005, background): “[15], [12], [20]) and requires more technical tools.”
Large deviations for Markovian nonlinear Hawkes processes (2011, background): “(For the theory of absolute continuity for point processes and its Girsanov formula, we refer to Lipster and Shiryaev [16].)”
Asset Prices with Heterogeneity in Preferences and Beliefs (2014, unknown): “7 In summary, our model differs from the standard Lucas (1978) model along two dimensions: one, preferences are heterogeneous; two, agents may not have the correct beliefs, and the beliefs of one agent may differ from those of the other.”
Estimation for discretely observed diffusions using transform functions (2003, background): “Estimation of continuously observed diffusions is well studied, see, for instance, Kutoyants (1984), Prakasa Rao (1999) or Liptser & Shiryaev (2001).”
On inference for partially observed nonlinear diffusion models using the Metropolis–Hastings algorithm (2001, methodology): “The likelihood function L(j; X) (with respect to P B ) is given by Girsanov's formula (see Liptster & Shiryayev 1978) as, L(j; X) / dP X dP B (x T ) = exp " Z T 0 b(x(t); ) 2 dx(t) ?”
Parameter estimation for Ornstein-Uhlenbeck processes driven by α-stable Lévy motions (2007, methodology): “Liptser, R.S. and Shiryaev, A.N. (2001).”
Statistical aspects of the fractional stochastic calculus (2006, background): “In fact the only di erence between the classical case (see [27]) and the fractional case is the presence of the constant p H in (43), (44), and (45).”