Related papers: Strong approximation of Bessel processes
We study the problem of approximating the Ising model partition function with complex parameters on bounded degree graphs. We establish a deterministic polynomial-time approximation scheme for the partition function when the interactions…
With reference to a baseline parametrization, we explore highly efficient fractional factorial designs for inference on the main effects and, perhaps, some interactions. Our tools include approximate theory together with certain carefully…
Consider the fractional Brownian Motion (fBM) $B^H=\{B^H(t): t \in [0,1] \}$ with Hurst index $H\in (0,1)$. We construct a probability space supporting both $B^H$ and a fully simulatable process $\hat B_{\epsilon}^H $ such that $$\sup_{t\in…
We introduce a variational theory for processes adapted to the multi-dimensional Brownian motion filtration that provides a differential structure allowing to describe infinitesimal evolution of Wiener functionals at very small scales. The…
We prove a Poisson process approximation result for stabilizing functionals of a determinantal point process. Our results use concrete couplings of determinantal processes with different Palm measures and exploit their association…
There are three main types of numerical computations for the Bessel function of the second kind: series expansion, continued fraction, and asymptotic expansion. In addition, they are combined in the appropriate domain for each. However,…
Variational mean field approximations tend to struggle with contemporary overparametrized deep neural networks. Where a Bayesian treatment is usually associated with high-quality predictions and uncertainties, the practical reality has been…
The 21st century has seen an enormous growth in the development and use of approximate Bayesian methods. Such methods produce computational solutions to certain intractable statistical problems that challenge exact methods like Markov chain…
The strong $L^2$-approximation of occupation time functionals is studied with respect to discrete observations of a $d$-dimensional c\`adl\`ag process. Upper bounds on the error are obtained under weak assumptions, generalizing previous…
Several problems in modeling and control of stochastically-driven dynamical systems can be cast as regularized semi-definite programs. We examine two such representative problems and show that they can be formulated in a similar manner. The…
Approximate Bayesian computation (ABC) is a simulation-based likelihood-free method applicable to both model selection and parameter estimation. ABC parameter estimation requires the ability to forward simulate datasets from a candidate…
The main purpose of this paper is to investigate the strong approximation of the integrated empirical process. More precisely, we obtain the exact rate of the approximations by a sequence of weighted Brownian bridges and a weighted Kiefer…
The paper deals with the fast-slow motions setups in the continuous time $\frac {dX^(t)}{dt}=\frac 1\varepsilon B(X^\varepsilon(t),\xi(t/\varepsilon^2))+b(X^\varepsilon(t),\,\xi(t/\varepsilon^2)),\, t\in [0,T]$ and the discrete time…
We propose an algorithm for Bayesian functional optimisation - that is, finding the function to optimise a process - guided by experimenter beliefs and intuitions regarding the expected characteristics (length-scale, smoothness, cyclicity…
It is a critical issue to compute the shortest paths between nodes in networks. Exact algorithms for shortest paths are usually inapplicable for large scale networks due to the high computational complexity. In this paper, we propose a…
Gaussian process models are commonly used as emulators for computer experiments. However, developing a Gaussian process emulator can be computationally prohibitive when the number of experimental samples is even moderately large. Local…
The (Non-Preemptive) Throughput Maximization problem is a natural and fundamental scheduling problem. We are given $n$ jobs, where each job $j$ is characterized by a processing time and a time window, contained in a global interval $[0,T)$,…
The method of self-similar factor approximants is completed by defining the approximants of odd orders, constructed from the power series with the largest term of an odd power. It is shown that the method provides good approximations for…
We address the problem of optimizing a Brownian motion. We consider a (random) realization $W$ of a Brownian motion with input space in $[0,1]$. Given $W$, our goal is to return an $\epsilon$-approximation of its maximum using the smallest…
Importance sampling of trajectories has proved a uniquely successful strategy for exploring rare dynamical behaviors of complex systems in an unbiased way. Carrying out this sampling, however, requires an ability to propose changes to…