Related papers: MEXIT: Maximal un-coupling times for stochastic pr…
The master equation and, more generally, Markov processes are routinely used as models for stochastic processes. They are often justified on the basis of randomization and coarse-graining assumptions. Here instead, we derive n-th order…
Markov jump processes are widely used to model natural and engineered processes. In the context of biological or chemical applications one typically refers to the chemical master equation (CME), which models the evolution of the probability…
Creation of entangled states of quantum systems with low decoherence rates is a cornerstone in practical implementation of quantum computations. Processes of separate dephasing in each qubit in experimentally feasible systems is commonly…
In recent work, Baez, Fong and the author introduced a framework for describing Markov processes equipped with a detailed balanced equilibrium as open systems of a certain type. These `open Markov processes' serve as the building blocks for…
In this paper we give a new approach to introduce switching strategies in a special class of optimal multiprocesses. Defined as the set of partitions of the time interval, switching strategies become the character of a classical control.…
We present a novel framework for performing statistical sampling, expectation estimation, and partition function approximation using \emph{arbitrary} heuristic stochastic processes defined over discrete state spaces. Using a highly parallel…
The past two decades have seen a revolution in statistical physics, generalizing it to apply to systems of arbitrary size, evolving while arbitrarily far from equilibrium. Many of these new results are based on analyzing the dynamics of the…
For two canonical examples of driven mesoscopic systems - a harmonically-trapped Brownian particle and a quantum dot - we numerically determine the finite-time protocols that optimize the compromise between the standard deviation and the…
Performing numerical integration when the integrand itself cannot be evaluated point-wise is a challenging task that arises in statistical analysis, notably in Bayesian inference for models with intractable likelihood functions. Markov…
A Markovian dichotomic system driven by a deterministic time-periodic force is analyzed in terms of the statistical properties of the switching events between the states. The consideration of the counting process of the switching events…
In this paper we study coupled fully non-local equations, where a linear non-local operator jointly acts on the time and space variables. We establish existence and uniqueness of the solution. A maximum principle is proved and used to…
We derive an equality for non-equilibrium statistical mechanics in finite-dimensional quantum systems. The equality concerns the worst-case work output of a time-dependent Hamiltonian protocol in the presence of a Markovian heat bath. It…
In multi-period stochastic optimization problems, the future optimal decision is a random variable whose distribution depends on the parameters of the optimization problem. We analyze how the expected value of this random variable changes…
In this paper, we propose a compositional approach for the construction of finite abstractions (a.k.a. finite Markov decision processes (MDPs)) for networks of discrete-time stochastic control subsystems that are not necessarily…
Let $(X_t)_{t \geq 0}$ be a continuous time Markov process on some metric space $M,$ leaving invariant a closed subset $M_0 \subset M,$ called the {\em extinction set}. We give general conditions ensuring either "Stochastic persistence"…
Time series datasets often contain heterogeneous signals, composed of both continuously changing quantities and discretely occurring events. The coupling between these measurements may provide insights into key underlying mechanisms of the…
Max-stable processes play an important role as models for spatial extreme events. Their complex structure as the pointwise maximum over an infinite number of random functions makes simulation highly nontrivial. Algorithms based on finite…
Isolating slower dynamics from fast fluctuations has proven remarkably powerful, but how do we proceed from partial observations of dynamical systems for which we lack underlying equations? Here, we construct maximally-predictive states by…
We consider the first exit time of a nonnegative Harris-recurrent Markov process from the interval $[0,A]$ as $A\to\infty$. We provide an alternative method of proof of asymptotic exponentiality of the first exit time (suitably…
We give a new method for generating perfectly random samples from the stationary distribution of a Markov chain. The method is related to coupling from the past (CFTP), but only runs the Markov chain forwards in time, and never restarts it…