Open Access
| Issue |
ESAIM: M2AN
Volume 54, Number 3, May-June 2020
|
|
|---|---|---|
| Page(s) | 811 - 844 | |
| DOI | https://doi.org/10.1051/m2an/2019077 | |
| Published online | 01 April 2020 | |
- L. Alili, P. Patie and J.L. Pedersen, Representations of the first hitting time density of an Ornstein-Uhlenbeck process. Stoch. Models 21 (2005) 967–980. [CrossRef] [Google Scholar]
- P. Baldi, L. Caramellino and M.G. Iovino, Pricing general barrier options: a numerical approach using sharp large deviations. Math. Finance 9 (1999) 293–322. [CrossRef] [Google Scholar]
- R.F. Bass, Diffusions and elliptic operators. In: Probability and its Applications (New York), Springer-Verlag, New York, 1998. [Google Scholar]
- A. Beskos and G.O. Roberts, Exact simulation of diffusions. Ann. Appl. Probab. 15 (2005) 2422–2444. [Google Scholar]
- A. Beskos, O. Papaspiliopoulos and G.O. Roberts, Retrospective exact simulation of diffusion sample paths with applications. Bernoulli 12 (2006) 1077–1098. [CrossRef] [MathSciNet] [Google Scholar]
- A. Beskos, O. Papaspiliopoulos and G.O. Roberts, A factorisation of diffusion measure and finite sample path constructions. Methodol. Comput. Appl. Probab. 10 (2008) 85–104. [Google Scholar]
- A.N. Borodin and P. Salminen, Handbook of Brownian motion – facts and formulae. Probability and its Applications. 2nd ed. Birkhäuser Verlag, Basel (2002). [CrossRef] [Google Scholar]
- M. Broadie, P. Glasserman and S. Kou, A continuity correction for discrete barrier options, Math. Finance 7 (1997) 325–349. [CrossRef] [Google Scholar]
- D.R. Cox and H.D. Miller, The Theory of Stochastic Processes. John Wiley & Sons Inc, New York (1965). [Google Scholar]
- D.A. Darling and A.J.F. Siegert, The first passage problem for a continuous Markov process, Ann. Math. Stat. 24 (1953) 624–639. [CrossRef] [Google Scholar]
- L. Devroye, Nonuniform Random Variate Generation. Springer-Verlag, New York (1986). [CrossRef] [Google Scholar]
- G. D’Onofrio and E. Pirozzi, Asymptotics of two-boundary first-exit-time densities for Gauss–Markov processes. Methodol. Comput. Appl. Probab. 21 (2019) 735–752. [Google Scholar]
- E. Gobet, Weak approximation of killed diffusion using Euler schemes. Stochastic Process. Appl. 87 (2000) 167–197. [CrossRef] [MathSciNet] [Google Scholar]
- E. Gobet and S. Menozzi, Stopped diffusion processes: boundary corrections and overshoot. Stochastic Process. Appl. 120 (2010) 130–162. [CrossRef] [Google Scholar]
- S. Herrmann and C. Zucca, Exact simulation of the first-passage time of diffusions. J. Sci. Comput. 79 (2019) 1477–1504. [Google Scholar]
- K. Itô and H.P. McKean, Diffusion Processes and Their Sample Paths. Second printing, corrected, Die Grundlehren der mathematischen Wissenschaften, Band 125. Springer-Verlag, Berlin-New York (1974). [Google Scholar]
- P.A. Jenkins, Exact simulation of the sample paths of a diffusion with a finite entrance boundary, Preprint arXiv:1311.5777 (2013). [Google Scholar]
- I. Karatzas and S.E. Shreve, Brownian motion and stochastic calculus, 2nd edition. In: Vol. 113 of Graduate Texts in Mathematics. Springer-Verlag, New York (1991). [Google Scholar]
- A. Lejay, Exitbm: a library for simulating Brownian motion’s exit times and positions from simple domains. Technical Report INRIA RR-7523 (2011). [Google Scholar]
- G.N. Milstein and M.V. Tretyakov, Simulation of a space-time bounded diffusion. Ann. Appl. Probab. 9 (1999) 732–779. [Google Scholar]
- L. Sacerdote, O. Telve and C. Zucca, Joint densities of first hitting times of a diffusion process through two time-dependent boundaries. Adv. Appl. Probab. 46 (2014) 186–202. [Google Scholar]
- E.T. Whittaker and G.N. Watson, A Course of Modern Analysis. Cambridge Mathematical Library. Reprint of the fourth (1927) edition. Cambridge University Press, Cambridge (1996). [CrossRef] [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.