Abstract
We focus on stochastic diffusion processes with jumps occurring at random times. After each jump the process is reset to a fixed state from which it restarts with a different dynamics. We analyze the transition probability density function, its moments and the first passage time density. The obtained results are used to study the lognormal diffusion process with jumps which is of interest in the applications.
This work was supported by INDAM-GNCS.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
di Cesare, R., Giorno, V., Nobile, A.G.: Diffusion processes subject to catastrophes. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds.) EUROCAST 2009. LNCS, vol. 5717, pp. 129–136. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-04772-5_18
Giorno, V., Nobile, A.G., di Cesare, R.: On the reflected Ornstein Uhlenbeck process with catastrophes. Appl. Math. Comput. 218, 11570–11582 (2012)
Giorno, V., Spina, S.: A Stochastic Gompertz model with jumps for an intermittent treatment in cancer growth. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds.) EUROCAST 2013. LNCS, vol. 8111, pp. 61–68. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-53856-8_8
Giorno, V., Nobile, A.G., Spina, S.: A note on time non-homogeneous adaptive queue with catastrophes. Appl. Math. Comput. 245, 220–234 (2014)
Giorno, V., Spina, S.: On the return process with refractoriness for non-homogeneous Ornstein-Uhlenbeck neuronal model. Math. Biosci. Eng. 11(2), 285–302 (2014)
Giorno, V., Spina, S.: Some remarks on stochastic diffusion processes with jumps. In: Lecture Notes of Seminario Interdisciplinare di Matematica, vol. 12, pp. 161–168 (2015)
Giorno, V., Román-Román, P., Spina, S., Torres-Ruiz, F.: Estimating a non-homogeneous Gompertz process with jumps as model of tumor dynamics. Comput. Stat. Data Anal. 107, 18–31 (2017)
Gutierrez, R., Gutierrez-Sanchez, R., Nafidi, A.: The trend of the total stock of the private car-petrol in Spain: stochastic modelling using a new gamma diffusion process. Appl. Energy 86, 18–24 (2009)
Nafidi, A., Gutierrez, R., Gutierrez-Sanchez, R., Ramos-Abalos, E., El Hachimi, S.: Modelling and predicting electricity consumption in Spain using the stochastic Gamma diffusion process with exogenous factors. Energy 113, 309–318 (2016)
Spina, S., Giorno, V., Román-Román, P., Torres-Ruiz, F.: A stochastic model of cancer growth subject to an intermittent treatment with combined effects: reduction of tumor size and rise of growth rate. Bull. Math. Biol. (2014). https://doi.org/10.1007/s11538-014-0026-8
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this paper
Cite this paper
Giorno, V., Spina, S. (2018). A Note on Diffusion Processes with Jumps. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds) Computer Aided Systems Theory – EUROCAST 2017. EUROCAST 2017. Lecture Notes in Computer Science(), vol 10672. Springer, Cham. https://doi.org/10.1007/978-3-319-74727-9_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-74727-9_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-74726-2
Online ISBN: 978-3-319-74727-9
eBook Packages: Computer ScienceComputer Science (R0)