Escudo de la República de Colombia Escudo de la República de Colombia

Cursillos y conferencias

Cursillos

Cursillo 1: Aplicaciones de cadenas de Markov en epidemiología y ecología.

   Carlos Moisés Hernández Suárez

                   Universidad de Colima, México

Día 1:

- Repaso de cadenas de Markov.

- Procesos de ramificación.

- Modelos de urnas.


Día 2.

- Aplicaciones de cadenas de Markov en Ecología.

- Se presentarán resultados desarrollados por el expositor para estimar los parámetros más importantes sobre la demografía de una población, como longevidad, R0,
tasa de crecimiento, tiempo inter- generacional etc., usando cadenas de Markov.


Día 3.

- Aplicaciones de Cadenas de Markov en epidemiología.

- En este día se presentarán resultados desarrollados por el expositor para calcular el tamaño de una epidemia en una población (número de infecciones o decesos) usando una nueva construcción de una epidemia. También se presentará un método muy simple para estimar el número reproductivo básico en modelos epidemiológicos complicados usando cadenas de Markov.

Cursillo 2: Computational models, tools and simulation for dynamics, prediction and control of infectious diseases.

Padmanabhan Seshaiyer

George Mason University,  EEUU

In this short course, we will introduce foundations of computational problem solving for mathematical models described by deterministic and stochastic differential equation systems. We start with an introductory course that will focus on foundations of computational problem solving with an overview on various state-of-the-art tools and techniques to solve a variety of applications. The second part will introduce diverse approaches for estimating parameters from real-data sets for prediction and control for deterministic problems modeling COVID-19 dynamics. These approaches will include standard numerical optimization approaches to disease informed neural network using PINNs and other Machine Learning approaches. The final part of the course will extend the applications to incorporating stochastic dynamics into the governing differential equations that describe COVID-19 dynamics. Participants will have the opportunity to work on a variety of software platforms during this three part course that includes:

Day 1: 

Foundations of Computational Problem Solving: Tools and Techniques

Day 2:

 Mathematical Models for Infectious Disease Dynamics: Prediction and Control - Part 1

Day 3:

 Mathematical Models for Infectious Disease Dynamics: Prediction and Control - Part 2

 

 

 

Cursillo 3: Self-similar stochastic processes in Wiener chaos.

Ciprian Tudor 

Université de Lille, Francia

 

The conference concerns a particular class of self-similar stochastic processes, the so-called Hermite processes. Self-similar processes are stochastic processes that are invariant in distribution under a suitable time scaling. The most known self-similar process is the fractional Brownian motion (fBm), which can be defined as the only Gaussian self-similar  process with stationary increments. Its stochastic analysis constitutes an important research direction in probability theory nowadays. The Hermite processes are non-Gaussian extensions of the fBm. These   processes, which are  are also self-similar,  with stationary increments and exhibit long-range dependence, have been also intensively studied in the last decades.  The purpose is to offer a rather detailed description of this class of stochastic processes and to discuss   some recent developments concerning their stochastic and statistical analysis. We analyze some    stochastic (partial) differential equations driven by a Hermite process, as well as the estimation of certain parameter in stochastic models with Hermite noise. Since the Hermite processes belongs to a Wiener chaos, we will also describe this concept.


Conferencias

Conferencia 1: Pedagogical innovations in education for transforming institutional practices in teaching and learning.

Conferencia 2: Positivity preserving schemes for non regular stochastic differential equations driven by fractional Brownian motion: the irregular case.

 Hector Araya

Universidad Adolfo Ibáñez
Viña del Mar, Chile

In this talk, we propose different schemes to approximate positive solutions of stochastic differential equations with non-lipschitz diffusion coefficient driven by fractional Brownian motion (fBm) with Hurst parameter H<1/2. Several numerical experiments are provided to illustrate the applicability of the proposed methods.

 

References


[1] Araya, H. (2022).Euler type scheme for the numerical approximation of non-lipschitz diffusion coefficient SDEs driven by fractional Brownian motion. Preprint.


[2] Coffie, E., Mao, X. & Proske, F. (2022). On the Analysis of a Generalised Rough Ait-Sahalia Interest Rate Model. Arxiv.


[3] Kubilius, K. (2020). Estimation of the Hurst index of the solutions of fractional SDE with locally Lipschitz drift. Nonlinear Analysis: Modelling and Control, 25(6), pp. 1059-1078.


[4] Zhang, S., & Yuan, C. (2021). Stochastic differential equations driven by fractional Brownian
motion with locally Lipschitz drift and their implicit Euler approximation. Proceedings of the
Royal Society of Edinburgh: Section A Mathematics, 151(4), 1278-1304.

Conferencia 3: Small time approximation in Wright-Fisher diffusion

Tania Roa

Universidad Adolfo Ibáñez,  Chile

El modelo de Wright-Fisher ha sido ampliamente utilizado para representar la variación aleatoria de la frecuencia alélica en el tiempo, debido a su forma simple, sin embargo una forma analítica cerrada para la distribución de la frecuencia alélica no ha sido construída. En este trabajo, presentamos dos aproximaciones para la distribución de la frecuencia alélica, utilizando herramientas de probabilidades. Las aproximaciones propuestas se adaptan bien al problema de la fijación o pérdida de un alelo, un problema que las distribuciones Gaussiana y beta, con parámetros adecuados, no son capaces de representar. Mediante un estudio de simulación demostramos, a través de la distancia de Hellinger y la norma L^2, que las aproximaciones propuestas son más eficientes, que las distribuciones Normal y Beta, para diferentes instantes generacionales.

 

Trabajo realizado por:

M. Fariello, IMERL, Universidad de La República, Montevideo, Uruguay.

G. Martínez, McGill University, Montreal, Canadá.

J. León, IMERL, Universidad de La República, Montevideo, Uruguay.

 

Referencias

[1] Dacunha-Castelle, D. and Florens-Zmirou, D, Estimation of the Coecients of a Diffusion from Discrete Observations, Stochastics, 19(4):263284, 1986.

[2] Epstein, C. L. and Mazzeo, R., Wright-Fisher Diffusion in One Dimension, SIAM Journal on Mathematical Analysis, 42(2):568608, 2010.

[3] OEwens, W. J., Mathematical Population Genetics, Springer, 2004.

 

 

 

Conferencia 4: Existence of optimal controls for stochastic Volterra equations.

Sergio Pulido

ENSIIE, París, Francia.

We study the existence of relaxed optimal controls in the weak formulation of control problems for stochastic Volterra equations (SVEs). Our study can be applied to rough processes which arise when the kernel appearing in the controlled SVE is singular at zero. This is joint work with Andrés Cárdenas and Rafael Serrano.
 

Sergio Pulido

Maître de Conférences (Associate Professor)

ENSIIE
1, square de la Résistance
91025 EVRY CEDEX
www.ensiie.fr