The Euler Scheme for L?evy Driven Stochastic Difierential Equations: Limit Theorems

By Jean Jacod. 2004

99 citations recorded by the source corpus.

Novel 2,4-bis-(trifluoromethyl)-6-nitrophenol compounds of the formula IN WHICH X is hydrogen; M; HNR 1R2R3; -COR4; -COOR5; N,N-dimethylaminocarbonyl; -SO2R6 or -CO-NH-R7; M is an equivalent of an alkali metal or alkaline earth metal, R1, R2 and R3 (individually) are hydrogen, alkyl, alkoxyalkyl, alkenyl, hydroxyalkyl, cycloalkyl, phenyalkyl, phenyl or substituted phenyl, R4 and R5 individually are alkyl, substituted alkyl, alkenyl, phenyl or substituted phenyl, R6 is alkyl, substituted alkyl, phenyl, substituted phenyl or dimethylamino, and R is alkyl, alkenyl, cycloalkyl, phenyl or substituted phenyl; ARE OUTSTANDINGLY EFFECTIVE SELECTIVE HERBICIDES.

Subfields: Applied Mathematics, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/60fe9cd7ff362d0633a9f9619d7b104984ae0274

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The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. V. Todorov
2. Nicolas G. Fournier
3. Rama Cont
4. Cecilia Mancini
5. Hongwei Long
6. Yaozhong Hu
7. F. Kühn
8. René L. Schilling

In Finance

1. V. Todorov
2. Cecilia Mancini
3. Rama Cont
4. Hongwei Long
5. Yaozhong Hu
6. Jean Jacod
7. Nicolas G. Fournier
8. Tim Bollerslev

In Management Science and Operations Research

1. V. Todorov
2. Nicolas G. Fournier
3. Cecilia Mancini
4. Rama Cont
5. Hongwei Long
6. Yaozhong Hu
7. F. Kühn
8. René L. Schilling

Citations in the corpus

• Asymptotic analysis of hedging errors in models with jumps (2009, unknown): “These results were later extended to Lévy-driven SDEs in [12,15].”
• Asymptotic properties of power variations of Lévy processes (2005, background): “When c = 0 if a CLT exists it is very complicated, and indeed it does not exist in general (see [9] for special examples of this situation): we do not consider those cases here at all.”
• Strong convergence of the Euler–Maruyama approximation for a class of Lévy-driven SDEs (2017, background): “[8] Jacod, J.: The Euler scheme for Lévy driven stochastic differential equations: Limit theorems.”
• Nonparametric tests for pathwise properties of semimartingales (2011, background): “2, which uses the fact that the speed of convergence to 0 of ∑n i=1 | ∫ ti ti−1 (Ms− −Mti−1) dMs| is shown in [12] to be un = n.”
• Parameter estimation for Ornstein-Uhlenbeck processes driven by α-stable Lévy motions (2007, methodology): “The Euler scheme for stochastic differential equations driven by Lévy processes has been well studied (see [5], [6], [7], [13] and the references therein).”
• Estimation of continuous-time stochastic volatility models with jumps using high-frequency data (2009, methodology): “For certain time-nonhomogeneous jump specifications, where Euler discretisation is needed, the results in Protter and Talay (1997), Jacod (2004) and Bruti-Liberati and Platen (2007) can be applied to prove the convergence of the simulated moment conditions to the true ones exactly as the proof of…”
• Rate of convergence of an empirical regression method for solving generalized backward stochastic differential equations (2006, unknown): “We refer to Jacod (2004) for other convergence results.”
• Simulation and approximation of Lévy-driven stochastic differential equations (2009, methodology): “Then for some a ∈ R, some b ∈ R+, and some measure ν on R∗ satisfying ∫ R∗ z2ν(dz) ∞, (1) Zt = at + bBt + ∫ t 0 ∫ R∗ zÑ(ds, dz), where (Bt)t≥0 is a standard Brownian motion, independent of a Poisson measure N(ds, dz) on [0,∞) × R∗ with intensity measure dsν(dz), and where Ñ is its compensated Po”