Related papers: A Piecewise Deterministic Markov Process via $(r,\…

We propose an approach to compute the boundary crossing probabilities for a class of diffusion processes which can be expressed as piecewise monotone (not necessarily one-to-one) functionals of a standard Brownian motion. This class…

We propose a new framework for imposing monotonicity constraints in a Bayesian nonparametric setting based on numerical solutions of stochastic differential equations. We derive a nonparametric model of monotonic functions that allows for…

The design of reliable indicators to anticipate critical transitions in complex systems is an im portant task in order to detect a coming sudden regime shift and to take action in order to either prevent it or mitigate its consequences. We…

In this paper, we consider a subclass of piecewise deterministic Markov processes with a Polish state space that involve a deterministic motion punctuated by random jumps, occurring in a Poisson-like fashion with some state-dependent rate,…

These lecture notes present some new concentration inequalities for Feynman-Kac particle processes. We analyze different types of stochastic particle models, including particle profile occupation measures, genealogical tree based evolution…

We consider a Markov process on a Riemannian manifold, which solves a stochastic differential equation in the interior of the manifold and jumps according to a deterministic reset map when it reaches the boundary. We derive a partial…

Graphical models express conditional independence relationships among variables. Although methods for vector-valued data are well established, functional data graphical models remain underdeveloped. We introduce a notion of conditional…

We construct a four-parameter family of Markov processes on infinite Gelfand-Tsetlin schemes that preserve the class of central (Gibbs) measures. Any process in the family induces a Feller Markov process on the infinite-dimensional boundary…

We consider the problem of flexible modeling of higher order hidden Markov models when the number of latent states and the nature of the serial dependence, including the true order, are unknown. We propose Bayesian nonparametric methodology…

In this paper we consider Bayesian parameter inference associated to a class of partially observed stochastic differential equations (SDE) driven by jump processes. Such type of models can be routinely found in applications, of which we…

We present an investigation of stochastic evolution in which a family of evolution equations in $L^1$ are driven by continuous-time Markov processes. These are examples of so-called piecewise deterministic Markov processes (PDMP's) on the…

We study invariant boundary conditions for one dimensional discrete Gaussian Markov processes, basic toy models of spatial Markov processes in statistical mechanics. More precisely, we give a decomposition of boundary objects in a non…

In this paper, we study a Markov chain-based stochastic gradient algorithm in general Hilbert spaces, aiming at approximating the optimal solution of a quadratic loss function. We establish probabilistic upper bounds on its convergence. We…

Dynamic heterogeneity has often been modeled by assuming that a single-particle observable, fluctuating at a molecular scale, is influenced by its coupling to environmental variables fluctuating on a second, perhaps slower, time scale.…

Variational quantum algorithms are poised to have significant impact on high-dimensional optimization, with applications in classical combinatorics, quantum chemistry, and condensed matter. Nevertheless, the optimization landscape of these…

Monte Carlo simulations of systems of particles such as hard spheres or soft spheres with singular kernels can display around a phase transition prohibitively long convergence times when using traditional Hasting-Metropolis reversible…

Dynamical processes can be transformed into graphs through a family of mappings called visibility algorithms, enabling the possibility of (i) making empirical data analysis and signal processing and (ii) characterising classes of dynamical…

The use of factor stochastic volatility models requires choosing the number of latent factors used to describe the dynamics of the financial returns process; however, empirical evidence suggests that the number and makeup of pertinent…

We extend the hypocoercivity framework for piecewise-deterministic Markov process (PDMP) Monte Carlo established in [Andrieu et. al. (2018)] to heavy-tailed target distributions, which exhibit subgeometric rates of convergence to…

From the Bayesian perspective, the category of conditional probabilities (a variant of the Kleisli category of the Giry monad, whose objects are measurable spaces and arrows are Markov kernels) gives a nice framework for conceptualization…