Related papers: Mixing it up: A general framework for Markovian st…
This paper is concerned with adaptive kernel estimation of the L\'evy density N(x) for bounded-variation pure-jump L\'evy processes. The sample path is observed at n discrete instants in the "high frequency" context (\Delta = \Delta(n)…
Interval Markov decision processes (IMDPs) generalise classical MDPs by having interval-valued transition probabilities. They provide a powerful modelling tool for probabilistic systems with an additional variation or uncertainty that…
We perform a detailed comparison between a Markov Switching Jump Diffusion Model and a Markov Switching {\alpha}-Stable Distribution Model with respect to the analysis of non-stationary data. We show that the jump diffusion model is…
We introduce a new method to accurately and efficiently estimate the effective dynamics of collective variables in molecular simulations. Such reduced dynamics play an essential role in the study of a broad class of processes, ranging from…
Many chemical reactions and molecular processes occur on timescales that are significantly longer than those accessible by direct simulation. One successful approach to estimating dynamical statistics for such processes is to use many short…
A new class of Markov chain Monte Carlo (MCMC) algorithms, based on simulating piecewise deterministic Markov processes (PDMPs), have recently shown great promise: they are non-reversible, can mix better than standard MCMC algorithms, and…
In this paper we model basketball plays as episodes from team-specific non-stationary Markov decision processes (MDPs) with shot clock dependent transition probabilities. Bayesian hierarchical models are employed in the modeling and…
Biochemical reactions can happen on different time scales and also the abundance of species in these reactions can be very different from each other. Classical approaches, such as deterministic or stochastic approach, fail to account for or…
A semi-Markov process method for obtaining general counting statistics for open quantum systems is extended to the scenario of resetting. The simultaneous presence of random resets and wave function collapses means that the quantum jump…
Discrete diffusion models, like continuous diffusion models, generate high-quality samples by gradually undoing noise applied to datapoints with a Markov process. Gradual generation in theory comes with many conceptual benefits; for…
The literature on statistical learning for time series often assumes asymptotic independence or "mixing" of the data-generating process. These mixing assumptions are never tested, nor are there methods for estimating mixing coefficients…
Semi-Markov processes play an important role in the effective description of partially accessible systems in stochastic thermodynamics. They occur, for instance, in coarse-graining procedures such as state lumping and when analyzing waiting…
We introduce a framework to approximate a Markov Decision Process that stands on two pillars: state aggregation -- as the algorithmic infrastructure; and central-limit-theorem-type approximations -- as the mathematical underpinning of…
In this work, a versatile mathematical framework for multi-state probabilistic modeling of Resistive Switching (RS) devices is proposed for the first time. The mathematical formulation of memristor and Markov jump processes are combined…
Upper estimates of densities of convolution semigroups of probability measures are given under explicit assumptions on the corresponding L\'evy measure and the L\'evy--Khinchin exponent.
The estimation of the L\'{e}vy density, the infinite-dimensional parameter controlling the jump dynamics of a L\'{e}vy process, is considered here under a discrete-sampling scheme. In this setting, the jumps are latent variables, the…
We analyse dynamical large deviations of quantum trajectories in Markovian open quantum systems in their full generality. We derive a {\em quantum level-2.5 large deviation principle} for these systems, which describes the joint…
We propose a new stochastic model for streamflow discharge timeseries as a jump-driven process, called a superposition of continuous-state branching processes with immigration (a supCBI process). It is a non-Markovian model having the…
The analysis of multiple time-to-event outcomes in a randomised controlled clinical trial can be accomplished with exisiting methods. However, depending on the characteristics of the disease under investigation and the circumstances in…
Studies of fixation dynamics in Markov processes predominantly focus on the mean time to absorption. This may be inadequate if the distribution is broad and skewed. We compute the distribution of fixation times in one-step birth-death…