Series Representations of Lévy Processes from the Perspective of Point Processes

By J. Rosínski. 2001

275 citations recorded by the source corpus.

Subfields: Management Science and Operations Research, Mathematical Physics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/4e91e54c1600ef7ca9a01c0c94bc0cec27fdbb67

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In Management Science and Operations Research

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Citations in the corpus

Distributional properties of the negative binomial Lévy process (2009, methodology): “Using the same notation, we can write the so-called shot noise representation of a standard gamma process (see [93]),”
Tempered stable distributions and processes in finance: numerical analysis (2010, methodology): “As emphasized in [21], the usual method of the inverse of Lévy measure [20] is difficult to implement, even if the spectral measure R has a simple form.”
Hölder regularity for operator scaling stable random fields (2007, background): “An overview on series representations of infinitely divisible random variable without Gaussian part can be found for example in [24, 26 ] and references therein.”
Estimation of continuous-time stochastic volatility models with jumps using high-frequency data (2009, methodology): “For the simulation of the jumps in the price and in the variance we use the series representation method (see Rosiński (2001)).”
Poisson Process Partition Calculus with applications to Exchangeable models and Bayesian Nonparametrics (2002, background): “…to see from an application of Khintchine’s (1937) Inverse Lévy method,[see also Ferguson and Klass (1972), Wolpert and Ickstadt (1998b), Sato (1999), Rosinski (2001), and Banjevic, Ishwaran and Zarepour (2002)], that the following identities hold; Proposition 5.5 (Distributional representations…”
Fractional Lévy processes with an application to long memory moving average processes (2006, methodology): “In fact, Rosinski (1989) provides immediately verifiable necessary conditions for interesting sample path properties.”
Monte Carlo Option Pricing for Tempered Stable (CGMY) Processes (2007, methodology): “For the tempered stable process (also known as CGMY model), an approximate simulation method based on Brownian subordination and a rejection method by Rosinski [11] was recently proposed by Madan and Yor [14] but, to the best of our knowledge, no exact simulation method for the increments of this pr”
Option Pricing in Stochastic Volatility Models of the Ornstein‐Uhlenbeck type (2003, background): “A self-contained exposition of the required results is given in Barndorff-Nielsen and Shephard (2001a), and recent developments are surveyed in Rosiński (2001).”
Jump-adapted discretization schemes for Lévy-driven SDEs (2010, background): “Sometimes, other approximations of Z by a compound Poisson process, such as the series representations [20] lead to simpler simulation algorithms (see Example 6).”
Gaussian approximation of multivariate Lévy processes with applications to simulation of tempered stable processes (2007, methodology): “Using Theorem 4.1 in Rosiński (2001) it is easy to verify that N is a compound Poisson process with E exp i〈y, N (t)〉 = exp { t ∫ Rd (ei〈y,x〉 − 1) ν (dx) } , where ν (B) = ∫ ∞ 0 F ({s ∈ S : H(r, s)1D (r, s) ∈ B \ {0}}) dr, B ∈ B(Rd).”
Some recent developments in stochastic volatility modelling (2002, background): “A self-contained exposition of the required results is given in Barndorff-Nielsen and Shephard (2001b), whereas recent developments are surveyed in Rosinski (2000) .”
On the Lamperti stable processes (2008, background): “This subordinator is also studied in Rivero [30], where the author finds its renewal density and other related computations.”