Dynamic models of long-memory processes driven by Lévy noise

By Vo Anh, Chris C. Heyde, Nikolai N. Leonenko. Journal of Applied Probability, 2002

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Ornstein–Uhlenbeck Processes and Extensions (2009, background): “The idea is to replace the dt and dBt differentials in (1) with the differentials of other semimartingales, or, alternatively, replace the exponential function and Brownian motion in (2) or (3) with other processes.”
Long range dependence in financial markets (2005, unknown): “By mixing these effects, one can construct self-similar processes where both long range dependence and heavy tails are present: fractional stable processes [64, 3 ] offer such examples.”
Lamperti-type laws (2007, background): “Then the density of W̃ is given by ηα,θ(x) = θ α e θ αR[ψ (1) R (x)(1 − 2α) + x2α[(ψ (1) R (x)) 2 θ α − ψ((2)) R (x)]] From this, we close with an interesting identity, Proposition 7.”
A continuous-time GARCH process driven by a Lévy process: stationarity and second-order behaviour (2004, methodology): “An alternative stochastic volatility model is introduced in Anh, Heyde and Leonenko [1], Section 5, who propose as volatility the stationary process”
Fractional Differential Equations Driven by Levy Noise (2003, background): “[2], will be recalled in the next section.”