Workshop Piecewise Deterministic Markov Processes and Applications

Thời gian: 09:00:01/07/2019 đến 17:00:05/07/2019

Địa điểm: VIASM, Ha Noi

Ban tổ chức (Organizing Committee)

Le Minh HA, Long Hoang NGO, Marc PEIGNE

Ban chương trình (Scientific Committee)

Jean-Stéphane DHERSIN, Long Hoang NGO, Marc PEIGNE

Cơ quan tổ chức và tài trợ (Host institution): VIASM, Ha Noi

Mục tiêu/ Nội dung (Objective or Description of the Scientific Content):

Piecewise Deterministic Markov Processes (PDMPs) are ubiquitous in the modeling of biological evolutions, and appear for example in the study of population dynamics, gene networks or neuronal activity. Their evolution is governed by a deterministic dynamics punctuated by random jumps. In particular, these processes do not possess a diffusive part. They are quite easy to construct but their study may reveal many surprises!

The aim of this 15 hour course is twofold.

  • We will present the construction and the main properties of PDMPs. To this end we will review classical Markovian techniques, and discuss the theory of stochastic persistence.
  • We will discuss in detail several examples. A first source of examples will come from biology, especially population dynamics. We will also explain how PDMPs can be used in Monte Carlo Markov Chain methods, both as a tool, for example to study the so-called meta-dynamics algorithm, and to devise new samplers, providing a competitive alternative to classical reversible Langevin dynamics.

1 Construction and basic properties of PDMP

1.1 Vector field, jump rate, jump measure, invariant measures

1.2 Examples (TCP Process, ON/OFF process, Zig-zag process)

2 General probabilistic tools

2.1 Coupling

2.2  Lyapunov functions

2.3 Persistence

3 Applications

3.1 TCP Process

3.2 MCMC: the zig-zag process and metadynamics

3.3 Switched Linear Ordinary Differential Equations

3.4 Population dynamics in a varying environment

Báo cáo mời: 

Florent MALRIEU, IDP, University of Tours, France, florent.malrieu@lmpt.univ-tours.fr

Pierre-André ZITT,  LAMA, University of Paris Est Marne La Vallée, France Pierre-Andre.Zitt@u-pem.fr

Thành phần tham dự (Expected participants): Researchers, PHD  and graduate students from Viet Nam. The last year bachelor students may also participate.

Đăng ký tham dự: https://viasm.edu.vn/hdkh/pdp2019?userkey=dang-ky-tham-du

Ngôn ngữ chính trong workshop (Language): English