Contributions to the Theory of Stochastic Processes and Their Applications

Supported by: Ministry of Science and Innovation, Government of Spain

Reference number: PID2021-125871NB-B-I00

Description: The main objective of CTPEyA (Spanish acronym of Contributions to the Theory of Stochastic Processes and Their Applications) is the development of three non-oriented lines of research in the field of Stochastic Processes and their Applications, that is, a relevant discipline within the Statistics and Operations Research area of knowledge.

Based on the mathematical, probabilistic and physical specialization of the research team at the Complutense University of Madrid and the National Distance Education University, and of the working group at the Universities of Leeds and Seville, and the Università degli Studi di Salerno, the general scientific objectives of the project are:

– Line 1: contribute to the theory on stochastic processes in the field of block-structured time-inhomogeneous Markov chains.
– Line 2: address applications of time-homogeneous and time-inhomogeneous Markov chains in Epidemiology and in Queueing Theory.
– Line 3: contribute to the theory on stochastic processes with general state space in the field of Itô and Stratonovich stochastic calculus, and in the field of block-structured Markov processes.

From the perspective of scientific cooperation, the CTPEyA project aims to be a suitable framework to explore new collaborations between the research team at the Complutense University of Madrid and the National University of Distance Education and researchers at the University of Oslo (B Oksendal; C di Nunno), University of California Santa Barbara (T Ichiba) and Politecnico di Milano (F Gazzola), among others, while reinforcing previously established collaborations with the researchers of the working group at the Universities of Leeds and Seville, and the Università degli Studi di Salerno. These collaborations are intended to facilitate research, innovation and training among the researchers involved, while adopting specific initiatives to facilitate the transfer of results.

Additionally, the CTPEyA project should be a suitable environment for the training of PhD students and the scientific dissemination of Mathematics in Society.

Keywords: Stochastic Processes; Stochastic Calculus

Scheduling dates: 01/09/2022-31/08/2025

Members of the UCM-UNED research team:

Collaborators at the UCM-UNED:

  • Mauricio Enrique Elizalde Mejía, postdoctoral researcher
  • María Gamboa Pérez, postdoctoral fellow

PhD students at the UCM-UNED:

  • Diana Taipe Hidalgo, predoctoral fellow at UCM
  • María Alejandra di Césare, PhD student at UNED
  • Helder Rojas Molina, PhD student at UNED

Collaborators outside the UCM-UNED:

Scientific papers:

Work in progress:

  • Gómez-Corral A, López-García M, Palacios-Rodríguez F (2024). Erlangian approximations in time-inhomogeneous quasi-birth-death processes.
  • Gómez-Corral A, López-García M, Taipe D (2024). Hitting probabilities and hitting times in time-inhomogeneous level-dependent quasi-birth-death processes.
  • Lopez-Herrero MJ, Mustaro V, Taipe D (2024). Analysis of incidence and time until disease detection in a stochastic model with vaccination and general transmission.
  • Lopez-Herrero MJ, Palacios-Rodríguez F (2024). Influence of asymptomatic infectious individuals in disease transmission: A stochastic approach.
  • Lopez-Herrero MJ, Taipe D (2024). The role of asymptomatic cases in the global incidence of an epidemic process subject to limited resources.
  • Gamboa M (2024). Analyzing total and peak simultaneous infections in outbreaks: SVIR modeling with partially effective and immunity loss over time vaccination.

Communications in scientific conferences:

  • (Invited talk) On the use of birth-death processes in the study of structured Markov chains, by A. Gómez-Corral. International Conference on Statistical Sciences & Stochastic Modelling, ICSSSM-2023. University of Calicut, Kerala, India.
  • (Contributed talk) Sufficient conditions for regularity, positive recurrence, and absorption in block-structured Markov chains, by A. Gómez-Corral. The 3rd International Workshop on Stochastic Processes and Their Applications, IWSPA 2023. University of Granada, Spain.
  • (Contributed talk) Some exact measures to quantify the potential transmission of an epidemic in a stochastic SVIS model with infection reintroduction and imperfect vaccine, by M. Gamboa and M.J. Lopez-Herrero. The 3rd International Workshop on Stochastic Processes and Their Applications, IWSPA 2023. University of Granada, Spain.
  • (Contributed talk) Honest versus insider trading, by C Escudero. The 3rd International Workshop on Stochastic Processes and Their Applications, IWSPA 2023. University of Granada, Spain.
  • (Contributed talk) Controlling population protection in stochastic SVIS models with imperfect vaccines, by MJ Lopez-Herrero. The 3rd International Workshop on Stochastic Processes and Their Applications, IWSPA 2023. University of Granada, Spain.
  • (Contributed talk) Quantifying infection transmission in a stochastic SVIS model with infection reintroduction when vaccine is partially effective, by M. Gamboa and M.J. Lopez-Herrero. The 14th International Conference on Dynamical Systems Applied to Biology and Natural Sciences, DSABNS 2023. The Basque Center for Applied Mathematics (BCAM), Spain.
  • (Contributed talk) Stochastic approach to study the loss of protection caused by an imperfect vaccine, by M. Gamboa and M.J. Lopez-Herrero. The 14th International Conference on Dynamical Systems Applied to Biology and Natural Sciences, DSABNS 2023. The Basque Center for Applied Mathematics (BCAM), Spain.
  • (Contributed talk) Modeling the propagation of an epidemic in a stochastic SVIS model when a re-vaccination of the susceptible population is considered,  by M. Gamboa and M.J. Lopez-Herrero.  The XIX Spanish Biometric Conference and VIII Iberoamerican Biometric Meeting, CEB-EIB 2023. University of Vigo, Spain.
  • (Contributed talk) Evolution of a deterministic SIS epidemic model with infection characteristics environmentally dependent, by M.J. Lopez-Herrero. 10th International Workshop on Applied Probability. IWAP2023. Thessaloniki, Greece.
  • (Contributed talk) On a stochastic epidemic model with limited number of hospital beds, by A. Gómez-Corral, M.J. Lopez-Herrero and D. Taipe. The 27th International Conference on Analytical & Stochastic Modelling Techniques & Applications, ASMTA 2023. University of Florence, Italy.
  • (Contributed talk) Sensitivity analysis of Markovian exact reproduction numbers, by M. Gamboa and M.J. Lopez-Herrero. International Conference of Computational Science and Its Applications, ICCSA 2023. National Technical University of Athens, Greece.
  • (Invited talk) Stochastic optimization in a Black-Scholes market under insider information, by C Escudero. EUROPT 2023, Corvinus University, Budapest, Hungary.
  • (Contributed talk) Número reproductivo básico en modelos de epidemias SIS con transmisión horizontal y vertical, by A Gómez-Corral, F Palacios-Rodríguez, MT Rodríguez-Bernal. XL Congreso Nacional de Estadística e Investigación Operativa, SEIO 2023. Elche, Spain.
  • (Contributed talk) Valores extremos y probabilidades de acceso en procesos QBD dependientes del nivel, by A Di Crescenzo, A Gómez-Corral, D Taipe. XL Congreso Nacional de Estadística e Investigación Operativa, SEIO 2023. Elche, Spain.
  • (Contributed talk) Study of antibiotic resistance by using Markov chains, by F Palacios-Rodríguez, F Chalub, A Gómez-Corral, M López-García. XL Congreso Nacional de Estadística e Investigación Operativa, SEIO 2023. Elche, Spain.
  • (Contributed talk) The number of inspections until the extinction of an epidemic in a discrete-time stochastic SIS-type model with some applications, by M Gamboa, MJ López-Herrero. XL Congreso Nacional de Estadística e Investigación Operativa, SEIO 2023. Elche, Spain.
  • (Contributed talk) Transmission of antibiotic-resistant bacteria explained with a Markov chain model, by F Chalub, A Gómez-Corral, M López-García, F Palacios-Rodríguez. CFE-CMStatistics 2023. Berlin, Germany.
  • (Plenary talk) Sensitivity analysis of the warning vaccination level for a stochastic SIVS model with imperfect vaccine, by MJ López-Herrero. International Conference on Advances in Applied Probability and Stochastic Processes – ICAAP&SP-2024. Thrissur, Kerala, India.
  • (Contributed talk) Extreme values and related hitting probabilities in epidemic models analyzed via level-dependent quasi-birth-death processes, by A Di Crescenzo, A Gómez-Corral, D Taipe. 15th Conference on Dynamical Systems Applied to Biology and Natural Sciences, DSABNS 2024. Lisbon, Portugal.
  • (Contributed talk) Disease incidence in a a stochastic SVI model with waning immunity, by MJ López-Herrero, D Taipe. Nineteenth International Conference on Computer Aided Systems Theory. EUROCAST 2024. Las Palmas de Gran Canaria, Spain.
  • (Contributed talk) Extreme values and hitting probabilities in LD-QBD processes, by A Di Crescenzo, A Gómez-Corral, D Taipe. Nineteenth International Conference on Computer Aided Systems Theory. EUROCAST 2024. Las Palmas de Gran Canaria, Spain.
  • (Invited talk) Level-dependent quasi-birth-death processes with applications in epidemics, by A D Crescezo, A Gómez-Corral, D Taipe. The 6th International Workshop on Branching Processes and Their Applications. IWBPA 2024. Badajoz, Spain.
  • (Contributed talk) Preserving herd immunity: A study on the impact of imperfect vaccines in the evolution of an epidemic process in non-isolated populations under a Markovian approach, by M Gamboa. Models in Population Dynamics, Ecology and Evolution. MPDEE-24. Leicester, UK.
  • (Contributed talk) Assessing the feasibility of a re-vaccination program when considering an imperfect vaccine under a Markovian approach, by M Gamboa. Conference on Stochastic Processes in Evolutionary Biology, 2024. Marseille, France.
  • (Contributed talk) Exact measures for quantifying the potential transmission of an epidemic process: A stochastic approach considering imperfect vaccines in an SVIR model, by M Gamboa, MJ López-Herrero, M López-García. 8th Stochastic Modelling Meeting. Milano, Italy.
  • (Contributed talk) Modelización de la resistencia a los antibióticos usando procesos estocásticos, by F Palacios-Rodríguez. VI Encuentro Conjunto RSME-SMM. Valencia, Spain.
  • (Contributed talk) Stochastic analysis of an epidemic model in a resource-limited environment (Minisymposium «New Directions for Stochastic Models of Epidemics»), by A Gómez-Corral, MJ López-Herrero, D Taipe. 13th European Conference on Mathematical and Theoretical Biology. ECMTB’24. Toledo, Spain.
  • (Contributed talk) On the exact and population bi-dimensional reproduction numbers in a stochastic SVIR model with imperfect vaccine, by M Gamboa, MJ López-Herrero. 13th European Conference on Mathematical and Theoretical Biology. ECMTB’24. Toledo, Spain.
  • (Contributed talk) On a Markovian epidemic model with limited resources, by A Gómez-Corral, MJ Lopez-Herrero, D Taipe. 4th International Workshop on Stochastic Processes and Their Applications. Zaragoza, Spain.
  • (Contributed talk) Quantifying the disease incidence in a stochastic SIVR model with waning immunity, by MJ Lopez-Herrero, D Taipe. 4th International Workshop on Stochastic Processes and Their Applications. Zaragoza, Spain.

Other contributions:

Popularization and dissemination of mathematics in epidemics:

  • (Course) Markov chains in Epidemiology, by A Gómez-Corral. NovaMath Thematic Week on Mathematical Models in Health. Universidade Nova de Lisboa, Portugal, July 2023.

Doctoral thesis

Related links: