Advertisement

A Note on Diffusion Processes with Jumps

  • Virginia Giorno
  • Serena SpinaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10672)

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.

References

  1. 1.
    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 CrossRefGoogle Scholar
  2. 2.
    Giorno, V., Nobile, A.G., di Cesare, R.: On the reflected Ornstein Uhlenbeck process with catastrophes. Appl. Math. Comput. 218, 11570–11582 (2012)MathSciNetzbMATHGoogle Scholar
  3. 3.
    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 CrossRefGoogle Scholar
  4. 4.
    Giorno, V., Nobile, A.G., Spina, S.: A note on time non-homogeneous adaptive queue with catastrophes. Appl. Math. Comput. 245, 220–234 (2014)MathSciNetzbMATHGoogle Scholar
  5. 5.
    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)MathSciNetzbMATHGoogle Scholar
  6. 6.
    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)Google Scholar
  7. 7.
    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)MathSciNetCrossRefGoogle Scholar
  8. 8.
    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)CrossRefGoogle Scholar
  9. 9.
    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)CrossRefGoogle Scholar
  10. 10.
    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

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Dipartimento di InformaticaUniversità di SalernoFiscianoItaly
  2. 2.Dipartimento di MatematicaUniversità di SalernoFiscianoItaly

Personalised recommendations