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In this paper we consider large state space continuous time Markov chains (MCs) arising in the field of systems biology. For density dependent families of MCs that represent the interaction of large groups of identical objects, Kurtz has…
Convection-diffusion-reaction equations are a class of second-order partial differential equations widely used to model phenomena involving the change of concentration/population of one or more substances/species distributed in space.…
We introduce diffusions on a space of interval partitions of the unit interval that are stationary with the Poisson-Dirichlet laws with parameters $(\alpha,0)$ and $(\alpha,\alpha)$. The construction has two steps. The first is a general…
Estimation of parameters of a diffusion based on discrete time observations poses a difficult problem due to the lack of a closed form expression for the likelihood. From a Bayesian computational perspective it can be casted as a missing…
Motivated by queues with many servers, we study Brownian steady-state approximations for continuous time Markov chains (CTMCs). Our approximations are based on diffusion models (rather than a diffusion limit) whose steady-state, we prove,…
In this paper we study a reflected Markov-modulated Brownian motion with a two sided reflection in which the drift, diffusion coefficient and the two boundaries are (jointly) modulated by a finite state space irreducible continuous time…
This paper develops the first class of algorithms that enable unbiased estimation of steady-state expectations for multidimensional reflected Brownian motion. In order to explain our ideas, we first consider the case of compound Poisson…
The time at which a one-dimensional continuous strong Markov process attains a boundary point of its state space is a discontinuous path functional and it is, therefore, unclear whether the exit time can be approximated by hitting times of…
Quantum processes describe concurrent communicating systems that may involve quantum information. We propose a notion of open bisimulation for quantum processes and show that it provides both a sound and complete proof methodology for a…
This paper proposes a bisimulation theory based on multiparty session types where a choreography specification governs the behaviour of session typed processes and their observer. The bisimulation is defined with the observer cooperating…
While there are many well-known and extensively tested results involving diffusion-limited binary reactions, reactions involving subdiffusive reactant species are far less understood. Subdiffusive motion is characterized by a mean square…
The challenging problem of conducting fully Bayesian inference for the reaction rate constants governing stochastic kinetic models (SKMs) is considered. Given the challenges underlying this problem, the Markov jump process representation is…
Hybrid Communicating Sequential Processes (HCSP) is a powerful formal modeling language for hybrid systems, which is an extension of CSP by introducing differential equations for modeling continuous evolution and interrupts for modeling…
Behind the nice unification provided by the notion of the level 2.5 in the field of large deviations for time-averages over a long Markov trajectory, there are nevertheless very important qualitative differences between the meaning of the…
We introduce a multivariate hidden Markov model to jointly cluster time-series observations with different support, i.e. circular and linear. Relying on the general projected normal distribution, our approach allows for bimodal and/or…
For discretisations of hyperbolic conservation laws, mimicking properties of operators or solutions at the continuous (differential equation) level discretely has resulted in several successful methods. While well-posedness for nonlinear…
Recent advances in diffusion$/$flow-matching policies have enabled imitation learning of complex, multi-modal action trajectories. However, they are computationally expensive because they sample a trajectory of trajectories: a…
The simulation of exit times for diffusion processes is a challenging task since it concerns many applications in different fields like mathematical finance, neuroscience, reliability... The usual procedure is to use discretiza-tion schemes…
We discuss velocity-jump models for chemotaxis of bacteria with an internal state that allows the velocity jump rate to depend on the memory of the chemoattractant concentration along their path of motion. Using probabilistic techniques, we…
Data collected by wearable devices in sports provide valuable information about an athlete's behavior such as their activity, performance, and ability. These time series data can be studied with approaches such as hidden Markov and…