1 |
E. Bacry, S. Delattre, M. Hoffmann, and J. F. Muzy, Some limit theorems for Hawkes processes and application to financial statistics, Stochastic Process. Appl. 123 (2013), no. 7, 2475-2499.
DOI
|
2 |
C. Bordenave and G. L. Torrisi, Large deviations of Poisson cluster processes, Stoch. Models 23 (2007), no. 4, 593-625.
DOI
|
3 |
P. Bremaud and L. Massoulie, Stability of nonlinear Hawkes processes, Ann. Probab. 24 (1996), no. 3, 1563-1588.
DOI
|
4 |
D. J. Daley and D. Vere-Jones, An Introduction to the Theory of Point Processes. Vol. I, second edition, Probability and its Applications (New York), Springer-Verlag, New York, 2003.
|
5 |
A. Dembo and O. Zeitouni, Large Deviations Techniques and Applications, second edition, Applications of Mathematics (New York), 38, Springer-Verlag, New York, 1998.
|
6 |
E. Errais, K. Giesecke, and L. R. Goldberg, Affine point processes and portfolio credit risk, SIAM J. Financial Math. 1 (2010), no. 1, 642-665.
DOI
|
7 |
R. Fierro, V. Leiva, and J. Moller, The Hawkes process with different exciting functions and its asymptotic behavior, J. Appl. Probab. 52 (2015), no. 1, 37-54.
DOI
|
8 |
X. Gao, X. Zhou, and L. Zhu, Transform analysis for Hawkes processes with applications in dark pool trading, Quant. Finance 18 (2018), no. 2, 265-282.
DOI
|
9 |
A. G. Hawkes and D. Oakes, A cluster process representation of a self-exciting process, J. Appl. Probability 11 (1974), 493-503.
DOI
|
10 |
A. G. Hawkes, Spectra of some self-exciting and mutually exciting point processes, Biometrika 58 (1971), 83-90.
DOI
|
11 |
P. Jagers, Branching Processes with Biological Applications, Wiley-Interscience, London, 1975.
|
12 |
T. Jaisson and M. Rosenbaum, Limit theorems for nearly unstable Hawkes processes, Ann. Appl. Probab. 25 (2015), no. 2, 600-631.
DOI
|
13 |
T. Jaisson and M. Rosenbaum, Rough fractional diffusions as scaling limits of nearly unstable heavy tailed Hawkes processes, Ann. Appl. Probab. 26 (2016), no. 5, 2860-2882.
DOI
|
14 |
A. Dassios and H. Zhao, A dynamic contagion process, Adv. in Appl. Probab. 43 (2011), no. 3, 814-846.
DOI
|
15 |
D. Karabash and L. Zhu, Limit theorems for marked Hawkes processes with application to a risk model, Stoch. Models 31 (2015), no. 3, 433-451.
DOI
|
16 |
B. Mehrdad and L. Zhu, On the Hawkes process with different exciting functions, Preprint. arXiv: 1403.0994 (2015).
|
17 |
Y. Seol, Limit theorems for the compensator of Hawkes processes, Statist. Probab. Lett. 127 (2017), 165-172.
DOI
|
18 |
Y. Seol, Limit theorems for discrete Hawkes processes, Statist. Probab. Lett. 99 (2015), 223-229.
DOI
|
19 |
Y. Seol, Limit theorems for inverse process of Hawkes process, Acta Math. Sin. (Engl. Ser.) 33 (2017), no. 1, 51-60.
DOI
|
20 |
Y. Seol, Moderate deviations for marked Hawkes processes, Acta Math. Sin. (Engl. Ser.) 33 (2017), no. 10, 1297-1304.
DOI
|
21 |
S. R. S. Varadhan, Large Deviations and Applications, CBMS-NSF Regional Conference Series in Applied Mathematics, 46, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1984.
|
22 |
S. Wheatley, V. Filimonov, and D. Sorrette, The Hawkes process with renewal immigration & its estimation with an EM algorithm, Computational Statistics & Data Analysis 94, 120-135 (2016).
DOI
|
23 |
L. Zhu, Central limit theorem for nonlinear Hawkes processes, J. Appl. Probab. 50 (2013), no. 3, 760-771.
DOI
|
24 |
L. Zhu, Moderate deviations for Hawkes processes, Statist. Probab. Lett. 83 (2013), no. 3, 885-890.
DOI
|
25 |
L. Zhu, Ruin probabilities for risk processes with non-stationary arrivals and subexponential claims, Insurance Math. Econom. 53 (2013), no. 3, 544-550.
DOI
|
26 |
L. Zhu, Limit theorems for a Cox-Ingersoll-Ross process with Hawkes jumps, J. Appl. Probab. 51 (2014), no. 3, 699-712.
DOI
|
27 |
L. Zhu, Process-level large deviations for nonlinear Hawkes point processes, Ann. Inst. Henri Poincare Probab. Stat. 50 (2014), no. 3, 845-871.
DOI
|
28 |
L. Zhu, Large deviations for Markovian nonlinear Hawkes processes, Ann. Appl. Probab. 25 (2015), no. 2, 548-581.
DOI
|