Related papers: Occupied Processes: Going with the Flow
The discrete class algorithm presented in this paper is an efficient simulation tool for stochastic processes governed by a reasonably small set of transition rates. The algorithm is presented, its performance compared to prevailing methods…
In this paper, we present an overview of the recent developments of functional quantization of stochastic processes, with an emphasis on the quadratic case. Functional quantization is a way to approximate a process, viewed as a…
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…
An important class of spatio-temporal models is constructed by leveraging the hierarchical structure of dynamical (or, state-space) models. This paper proposes a new statistical dynamical model for spatio-temporal processes motivated by…
Financial structures such as securitisations, insurance contracts, and other hierarchical claims systems can be interpreted as deterministic allocation mechanisms acting on stochastic inflow processes. This paper develops a general…
Robust estimates for the performance of complicated queueing networks can be obtained by showing that the number of jobs in the network is stochastically comparable to a simpler, analytically tractable reference network. Classical coupling…
The Shape Calculus is a bio-inspired calculus for describing 3D shapes moving in a space. A shape forms a 3D process when combined with a behaviour. Behaviours are specified with a timed CCS-like process algebra using a notion of channel…
ODE solvers with randomly sampled timestep sizes appear in the context of chaotic dynamical systems, differential equations with low regularity, and, implicitly, in stochastic optimisation. In this work, we propose and study the stochastic…
In the Time-Windows Unsplittable Flow on a Path problem (twUFP) we are given a resource whose available amount changes over a given time interval (modeled as the edge-capacities of a given path $G$) and a collection of tasks. Each task is…
A central problem of Quantitative Finance is that of formulating a probabilistic model of the time evolution of asset prices allowing reliable predictions on their future volatility. As in several natural phenomena, the predictions of such…
We derive an equation to compute directly the expected occupation time of the centered Ornstein-Uhlenbeck process. This allows us to identify the parameters of the Ornstein-Uhlenbeck process for available occupation times via a standard…
This paper develops a generalization of Brownian motion with stationary, autocorrelated increments as a tractable model for problems in business and finance. We show that any real continuous Gaussian Markov process with stationary…
Interval scheduling is a basic problem in the theory of algorithms and a classical task in combinatorial optimization. We develop a set of techniques for partitioning and grouping jobs based on their starting and ending times, that enable…
For decades, uncertainty quantification techniques based on the spectral approach have been demonstrated to be computationally more efficient than the Monte Carlo method for a wide variety of problems, particularly when the dimensionality…
We propose new continuous-time formulations for first-order stochastic optimization algorithms such as mini-batch gradient descent and variance-reduced methods. We exploit these continuous-time models, together with simple Lyapunov analysis…
Markov jump processes are continuous-time stochastic processes with a wide range of applications in both natural and social sciences. Despite their widespread use, inference in these models is highly non-trivial and typically proceeds via…
In this paper, a class of non-Markovian forward-backward doubly stochastic systems is studied. By using the technique of functional It\^o (or path-dependent) calculus, the relationship between the systems and related path-dependent…
Markov Decision Processes (MDPs) have been used to formulate many decision-making problems in science and engineering. The objective is to synthesize the best decision (action selection) policies to maximize expected rewards (or minimize…
The neural ordinary differential equation (ODE) framework has emerged as a powerful tool for developing accelerated surrogate models of complex physical systems governed by partial differential equations (PDEs). A popular approach for PDE…
The dynamics of the eigenvalues (semimartingales) of a L\'{e}vy process $X$ with values in Hermitian matrices is described in terms of It\^{o} stochastic differential equations with jumps. This generalizes the well known Dyson-Brownian…