PUBLICATIONS OF THE LAST YEARS
M. Abundo: Study of direct and inverse first-exit problems for drifted Brownian motion with Poissonian resetting.
Methodol Comput Appl Probab 27, 89 (2025). https://doi.org/10.1007/s11009-025-10216-z
M. Abundo: Inverse First-Passage Problems of a Diffusion with Resetting.
Theor. Probability and Math. Statist. No. 112, 2025, Pages 17-36. doi.org/10.1090/tpms/1225. Published electronically: May 9, 2025
M. Abundo (Ed.): Special Issue Reprint Stochastic Modeling in Biological System
mdpi.com/journal/fractalfract. MDPI Basel, Switzerland ISBN 978-3-7258-1241-7 (Hbk) ISBN 978-3-7258-1242-4 (PDF)
doi.org/10.3390/books978-3-7258-1242-4 (2024).
M. Abundo: The first-passage area of a Wiener process with stochastic resetting.
Methodol Comput Appl Probab (2023) 25:92 https://doi.org/10.1007/s11009-023-10069-4
M. Abundo, E. Pirozzi: On the Estimation of the Persistence Exponent for a Fractionally
Integrated Brownian Motion by Numerical Simulations. Fractal Fract. 2023, 7, 107.
https://doi.org/10.3390/fractalfract7020107
M. Abundo: Asymptotic of the running maximum distribution of a Gaussian Bridge.
(2022) Stochastic Analysis and Applications.
Published online: 19 September 2022; pg.. 1-20. DOI:10.1080/07362994.2022.2123344
https://www.tandfonline.com/eprint/AVZ8GTNF7XVAKSNSQI7C/full?target=10.1080/07362994.2022.2123344
M. Abundo: Some examples of solutions to an inverse problem for the first-passage place of a
jump-diffusion process. Control & Cybernetics Vol. 51 (2022) No. 1, pg. 31-42.
DOI: 10.2478/candc-2022-000373.
M. Abundo: The first-passage area of Ornstein-Uhlenbeck process revisited. (2021).
Stochastic Analysis and Applications. Published online: 28 Dec 2021; pg. 1-19. DOI: 10.1080/07362994.2021.2018335
https://www.tandfonline.com/eprint/GDYPA5GKHXW27RN6WUDK/full?target=10.1080/07362994.2021.2018335
M. Abundo, E. Pirozzi: Fractionally Integrated Gauss-Markov processes and applications.
Communications in Nonlinear Science and Numerical Simulation (2021),
doi: https://doi.org/10.1016/j.cnsns.2021.105862 (arXiv:1905.08167 1905.081167.pdf )
M. Abundo, E. Pirozzi: On the Entropy of Fractionally Integrated Gauss-Markov Processes.
Mathematics 2020, 8(11), 2031; https://doi.org/10.3390/math8112031
M. Abundo: On the first-passage times of certain Gaussian processes, and related asymptotics.
Stochastic Analysis and Applications. Published online: 09 Nov 2020. https://doi.org/10.1080/07362994.2020.1843495
https://www.tandfonline.com/eprint/DHJTBKFZ5DBG7XI53VBU/full?target=10.1080/07362994.2020.1843495
M. Abundo: An inverse problem for the first-passage place of some diffusion processes with random starting point.
Stochastic Analysis and Applications 2020, VOL. 38, No. 6, 1122–1133 https://doi.org/10.1080/07362994.2020.1768867
https://www.tandfonline.com/eprint/HSBSAGSGYYVUTU8SWGCP/full?target=10.1080/07362994.2020.1768867
M. Abundo, M. B. Scioscia Santoro: On the successive passage times of certain one-dimensional diffusions.
Lecture Notes in Computer Science (LNCS), 12013, EUROCAST 2019. R. Moreno-D´ıaz et al. (Eds.) ; pp. 1–9, 2020.
https://doi.org/10.1007/978-3-030-45093-9_24
M. Abundo: Randomization of a linear boundary in the first-passage problem of Brownian motion.
Stochastic Analysis and Applications. Published online: 26 Nov 2019 https://doi.org/10.1080/07362994.2019.1695629
M. Abundo, E. Pirozzi: On the Integral of the Fractional Brownian Motion and Some Pseudo-Fractional Gaussian Processes.
Mathematics 2019, 7(10), 991, 1–12; https://doi.org/10.3390/math7100991
M. Abundo, G. Ascione, M.F. Carfora, E. Pirozzi: A fractional PDE for first passage time of time-changed Brownian motion
and its numerical solution. Accepted for publication in Applied Numerical Mathematics (2019).
M. Abundo: An inverse first-passage problem revisited: the case of fractional Brownian motion, and time-changed Brownian motion.
Stochastic Analysis and Applications, 2019, vol. 37, No. 5, 708–716. https://www.tandfonline.com/eprint/NDDZJQUEKQFHRTQJU5VF/full?target=10.1080/07362994.2019.1608834
M. Abundo, S. Furia: Joint Distribution of First-Passage Time and First-Passage Area of
Certain Lèvy Processes. Methodol Comput Appl Probab https://doi.org/10.1007/s11009-018-9677-5
M. Abundo: The Randomized First-Hitting Problem of Continuously Time-Changed Brownian Motion.
Mathematics 2018 6(6), 91, 1–10. https://doi.org/10.3390/math6060091
M. Abundo, M. Abundo: Some Remarks on the Mean of the Running maximum of
Integrated Gauss-Markov Processes and Their First-Passage Times.
In: Computer Science ( LNCS) 10672, Computer Aided Systems Theory.
R. Moreno-Diaz et al. (Eds.): EUROCAST 2017, Part II, LNCS 10672, pp. 72–79, 2018.
https://doi.org/10.1007/978-3-319-74727-9_9
M. Abundo, E. Pirozzi: Integrated Stationary Ornstein-Uhlenbeck Process, and Double
Integral Processes. Physica A 494 (2018) 265–275. doi.org/10.1016/j.physa.2017.12.043
M. Abundo: The arctangent law for a certain random time related to one-dimensional
diffusions. Stochastic Analysis and Applications, 36(1), 181–187 (2018).
https://doi.org/10.1080/07362994.2017.1387565
M. Abundo, D. Del Vescovo: On the joint distribution of first-passage time and
first-passage area of drifted Brownian motion. Methodol Comput Appl Probab (2017)
19:985–996 DOI 10.1007/s11009-017-9546-7 (Online first 25 Jan 2017).
M. Abundo: The mean of the running maximum of an integrated Gauss-Markov
process and the connection with its first-passage time. Stochastic Anal. Appl.
35:3, 499-510, 2017. http://dx.doi.org/10.1080/07362994.2016.1273784
M. Abundo: On the excursions of drifted Brownian motion and the successive passage times of
Brownian motion. Physica A 457 (2016) 176–182. doi:10.1016/j.physa.2016.03.052
M. Abundo: An overview on inverse first-passage-time problems for one-dimensional diffusion
processes. Lecture Notes of Seminario Interdisciplinare di Matematica Vol. 12 (2015)
pp. 1 – 44. http://dimie.unibas.it/site/home/info/documento3012448.html
M. Abundo: A randomized first-passage problem for drifted Brownian motion subject
to hold and jump from a boundary. Stochastic Anal. Appl. 34(1): 38-46, 2016. DOI:10.1080/073629942015.1099047
M. Abundo: On the first-passage time of an integrated Gauss-Markov process.
Scientiae Mathematicae Japonicae Online, e-2015, 28, 1-14
M. Abundo: One-dimensional reflected diffusions with two boundaries and an inverse first-
hitting problem. Stochastic Anal. Appl. 32: 975–991, 2014.
DOI 10.1080/07362994.2014.959595
M. Abundo: Investigating the Distribution of the First-Crossing Area of a Diffusion Process
with Jumps Over a Threshold. The Open Applied Mathematics Journal, 2013, 7, 18-28.
DOI: 10.2174/1874114201307010018
M. Abundo, M. Abundo: Some Remarks on the First-Crossing Area of a Diffusion Process
with Jumps over a Constant Barrier. Lecture Notes in Computer Science, Computer Aided
Systems Theory.EUROCAST 2013, Part I. vol. 8111, pp. 20-27. Springer Berlin/ Heidelberg,
2013. DOI 10.1007/978-3-642-53856-8
M. Abundo: On the representation of an integrated Gauss-Markov process.
Scientiae Mathematicae Japonicae Online, e-2013, 719–723
M. Abundo: Solving an inverse first-passage-time problem for Wiener process subject to
random jumps from a boundary. Stochastic Anal. Appl. 31: 4, 695-707, 2013.
ISSN 0736-2994 print/1532-9356 online. DOI: 10.1080/07362994.2013.800358
M. Abundo: Some randomized first-passage problems for one-dimensional diffusion
processes. Scientiae Mathematicae Japonicae, 76, No. 1 (2013), 33–46 : e-2013, 33–46.
M. Abundo: The double-barrier inverse first-passage problem for Wiener process with random
starting point. Statistics and Probability Letters. Available online Sept 2012,
vol. 83 (2013), 168-176. doi: 10.1016/j.spl.2012.09.006.
M. Abundo, C. Macci, G. Stabile: Asymptotic results for exit probabilities of stochastic processes
governed by an integral type rate function. Prob. Math. Statis. Vol. 32, (1), (2012), 25-39.
M. Abundo: First-passage time of a stochastic integral process trough a linear boundary.
International Journal of Applied Mathematics (IJAM), vol. 25, No 1, (2012), 41-49.
M. Abundo: An inverse first-passage problem for one-dimensional diffusions with random
starting point. Statistics and Probability Letters, 82 (1) (2012), 7-14. doi.org/10.1016/j.spl.2011.09.005
M. Abundo: On the first-passage area of a one-dimensional jump-diffusion process.
Methodol. Comput. Appl. Probab. (2011). Online First, April 2011: DOI 10.1007/s11009-011-9223-1.
M. Abundo, M. Abundo: The first-passage area of an emptying Brownian queue.
International Journal of Applied Mathematics (IJAM), vol. 24, No 2, (2011), 259-266.
M. Abundo: First-Passage Problems for one-dimensional diffusions with random jumps from a boundary.
Stochastic Anal. Appl. 29 (1) (2011), 121- 145.
M. Abundo: First-Passage Problems for Asymmetric Diffusions and Skew-diffusion Processes
Open Systems & Information Dynamics Vol. 16, No. 4 (2009), 325-350.
M. Abundo: On the Continuous Diffusion Approximation of Some Discrete Markov Chains
The Open Applied Mathematics Journal, 2009, 3, 7-13.
M. Abundo: On the First Hitting Time of a One-dimensional Diffusion and a Compound Poisson Process
Methodol. Comput. Appl. Probab. (2010) 12:473–490 (Online First, 2008: DOI 10.1007/s11009-008-9115-1).
M. Abundo: On the distribution of the time average of a jump-diffusion process
International Journal of Applied Mathematics (IJAM), vol. 21, No. 3 (2008), 447-454.
M. Abundo: Some Remarks on the maximum of a one-dimensional diffusion process.
Prob. Math. Statis. vol 28 (1) (2008), 107-120.
M. Abundo: On first-passage problems for asymmetric one-dimensional diffusions.
Lecture Notes in Computer Science, Computer Aided Systems Theory – EUROCAST 2007, vol. 4739,
pp. 179-186, Springer Berlin/ Heidelberg, 2007.
M. Abundo: Limit at zero of the first-passage time density and the inverse problem for one-
dimensional diffusions. Stochastic Anal. Appl., 24 (2006), 1119-1145.
M. Abundo: The arc-sine law for the first instant at which a diffusion process equals the ultimate
value of a functional Int. J. Pure Appl. Math., 30 (1), 13-22 (2006).
M. Abundo: Qualitative behaviour of the first-passage-time density of a one-dimensional
diffusion over a moving boundary Scientiae Mathematicae Japonicae, 64, No. 2 (2006), 199-216,
:e-2006, 641-658.
M. Abundo: Stopping a stochastic integral process as close as possible to the ultimate value of a
functional Scientiae Mathematicae Japonicae , 60 No. 3 (2004), 475-479,: e-2004, (10) 417-421.
M. Abundo: On the risk of extinction for a population subject to a random markov evolution with
jumps Open Sys. & Information Dyn. 11, 105-121 (2004).
M. Abundo: On the first-passage time of diffusion processes over a one-sided stochastic boundary.
Stochastic Analysis and Applications vol. 21, No. 1, 1-23 (2003).
M. Abundo: Some comparison results of solutions of diffusion and jump-diffusion equations.
Advances and Applications in Statistics vol. 2 (1), 51-78 (2002).
M. Abundo: Some conditional crossing results of Brownian motion over a piecewise-linear
boundary. Statistics and Probability Letters, vol. 58 (2), 131-145 (2002).
M. Abundo, L. Accardi, N. Rosato, L. Stella: Analysing protein energy data by a stochastic
model for cooperative interactions: comparison and characterization of cooperativity.
J. Math. Biol. 44, 341-359 (2002).
M. Abundo: On comparison of solutions of diffusion and jump-diffusion equations
In: R. Trappl (Ed.) Cybernetics and Systems 2002 , pp 307-312, Austrian Society for
Cybernetics Studies, Vienna, 2002.
M. Abundo: On first-passage-times for one-dimensional jump-diffusion processes.
Prob. Math. Statis., vol 20, Fasc. 2, 399-423 (2000).
M. Abundo: Some results about boundary crossing for Brownian motion.
Ricerche di Matematica vol. L, (2), 283-301 (2001).
M. Abundo: On first-crossing times of one-dimensional diffusions over two time-dependent
boundaries. Stochastic Analysis and Applications. , 18 (2), 179-200 (2000).