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We analyze and compare the computational complexity of different simulation strategies for Monte Carlo in the setting of classically scaled population processes. This allows a range of widely used competing strategies to be judged…
Bisimulation metrics are powerful tools for measuring similarities between stochastic processes, and specifically Markov chains. Recent advances have uncovered that bisimulation metrics are, in fact, optimal-transport distances, which has…
The simulation of chemical kinetics involving multiple scales constitutes a modeling challenge (from ordinary differential equations to Markov chain) and a computational challenge (multiple scales, large dynamical systems, time step…
Approximating the stationary probability of a state in a Markov chain through Markov chain Monte Carlo techniques is, in general, inefficient. Standard random walk approaches require $\tilde{O}(\tau/\pi(v))$ operations to approximate the…
Liquid State Machine (LSM) is a brain-inspired architecture used for solving problems like speech recognition and time series prediction. LSM comprises of a randomly connected recurrent network of spiking neurons. This network propagates…
First passage time (FPT) is the time a particle, subject to some stochastic process, hits or crosses a closed surface for the very first time. $\tau$-leaping methods are a class of stochastic algorithms in which, instead of simulating every…
A new method of the stochastic simulation algorithm (SSA), named the Hashing-Leaping method (HLM), for exact simulations of a class of Markov jump processes, is presented in this paper. The HLM has a conditional constant computational cost…
There has been an increasing demand for formal methods in the design process of safety-critical synthetic genetic circuits. Probabilistic model checking techniques have demonstrated significant potential in analyzing the intrinsic…
We consider continuous time Markovian processes where populations of individual agents interact stochastically according to kinetic rules. Despite the increasing prominence of such models in fields ranging from biology to smart cities,…
Markov jump processes (or continuous-time Markov chains) are a simple and important class of continuous-time dynamical systems. In this paper, we tackle the problem of simulating from the posterior distribution over paths in these models,…
We propose a novel, tractable latent state inference scheme for Markov jump processes, for which exact inference is often intractable. Our approach is based on an entropic matching framework that can be embedded into the well-known…
We develop a computational method for expected functionals of the drawdown and its duration in exponential L\'evy models. It is based on a novel simulation algorithm for the joint law of the state, supremum and time the supremum is attained…
There is a great need for accurate and efficient computational approaches that can account for both the discrete and stochastic nature of chemical interactions as well as spatial inhomogeneities and diffusion. This is particularly true in…
Stochastic models of biochemical reaction networks are widely used to capture intrinsic noise in cellular systems. The typical formulation of these models are based on Markov processes for which there is extensive research on efficient…
This paper is concerned with the development of rigorous approximations to various expectations associated with Markov chains and processes having non-stationary transition probabilities. Such non-stationary models arise naturally in…
There exist several methods for simulating biological and physical systems as represented by chemical reaction networks. Systems with low numbers of particles are frequently modelled as discrete-state Markov jump processes and are typically…
Markov processes are widely used mathematical models for describing dynamic systems in various fields. However, accurately simulating large-scale systems at long time scales is computationally expensive due to the short time steps required…
The aim of this paper is to approximate a finite-state Markov process by another process with fewer states, called herein the approximating process. The approximation problem is formulated using two different methods. The first method,…
Quasi-2D Coulomb systems are of fundamental importance and have attracted much attention in many areas nowadays. Their reduced symmetry gives rise to interesting collective behaviors, but also brings great challenges for particle-based…
The numerical simulation of dynamical phenomena in interacting quantum systems is a notoriously hard problem. Although a number of promising numerical methods exist, they often have limited applicability due to the growth of entanglement or…