Related papers: A pseudo-Markov property for controlled diffusion …

A new formulation of Stochastic Model Predictive Output Feedback Control is presented and analyzed as a translation of Stochastic Optimal Output Feedback Control into a receding horizon setting. This requires lifting the design into a…

We consider a rate control problem for an $N$-particle weakly interacting finite state Markov process. The process models the state evolution of a large collection of particles and allows for multiple particles to change state…

Scientific inference involves obtaining the unknown properties or behavior of a system in the light of what is known, typically, without changing the system. Here we propose an alternative to this approach: a system can be modified in a…

Bisimulation is a concept that captures behavioural equivalence of states in a variety of types of transition systems. It has been widely studied in discrete-time settings where a key notion is the bisimulation metric which quantifies "how…

We analyze the problem of stochastic optimal control of SDEs where the driver includes a self-exciting stochastic process. Due to the non-Markovian nature of the problem, we apply the stochastic maximum principle approach. We derive a…

In this paper we propose a (sub)distribution-based bisimulation for labelled Markov processes and compare it with earlier definitions of state and event bisimulation, which both only compare states. In contrast to those state-based…

In this paper we set up an optimal control framework for a hybrid stochastic system with dual or multiple Markov switching diffusion processes, while Markov chains governing these switching diffusions are not identical as assumed by the…

In this paper we consider non convex control problems of stochastic differential equations driven by relaxed controls. We present existence of optimal controls and then develop necessary conditions of optimality. We cover both continuous…

We study the optimal control of discrete time mean filed dynamical systems under partial observations. We express the global law of the filtered process as a controlled system with its own dynamics. Following a dynamic programming approach,…

Recently, several powerful tools for the reconstruction of stochastic differential equations from measured data sets have been proposed [e.g. Siegert et al., Physics Letters A 243, 275 (1998); Hurn et al., Journal of Time Series Analysis…

In this paper, we study the asymptotic of exit problem for controlled Markov diffusion processes with random jumps and vanishing diffusion terms, where the random jumps are introduced in order to modify the evolution of the controlled…

We consider the problem of learning two families of time-evolving random measures from indirect observations. In the first model, the signal is a Fleming--Viot diffusion, which is reversible with respect to the law of a Dirichlet process,…

This paper is divided into two parts. The first part reviews the formulae for f-divergences in the study of continuous-time Markov processes and explores their applications in areas such as stochastic stability, the second law of…

In this paper, we investigate the exact controllability properties of an advection-diffusion equation on a bounded domain, using time- and space-dependent velocity fields as the control parameters. This partial differential equation (PDE)…

This paper aims to provide a simple modelling of speculative bubbles and derive some quantitative properties of its dynamical evolution. Starting from a description of individual speculative behaviours, we build and study a second order…

We consider a stochastic process which is (a) described by a continuous-time Markov chain on only short time-scales and (b) constrained to conserve a number of hidden quantities on long time-scales. We assume that the transition matrix of…

To describe and analyze the dynamics of Self-Organized Criticality (SOC) systems, a four-state continuous-time Markov model is proposed in this paper. Different to computer simulation or numeric experimental approaches commonly employed for…

We first prove a mimicking theorem (also known as a Markovian projection theorem) for the marginal distributions of an Ito process conditioned to not have exited a given domain. We then apply this new result to the proof of a conjecture of…

"Quantum trajectories" are solutions of stochastic differential equations of non-usual type. Such equations are called "Belavkin" or "Stochastic Schr\"odinger Equations" and describe random phenomena in continuous measurement theory of Open…

The distribution of a Markov process with killing, conditioned to be still alive at a given time, can be approximated by a Fleming-Viot type particle system. In such a system, each particle is simulated independently according to the law of…