Related papers: Approximation of stationary processes and Toeplitz…
In this work, we propose a novel method for quantifying distances between Toeplitz structured covariance matrices. By exploiting the spectral representation of Toeplitz matrices, the proposed distance measure is defined based on an optimal…
In this article we develop a new methodology to prove weak approximation results for general stochastic differential equations. Instead of using a partial differential equation approach as is usually done for diffusions, the approach…
Partially observable Markov decision processes (POMDPs) provide an elegant mathematical framework for modeling complex decision and planning problems in stochastic domains in which states of the system are observable only indirectly, via a…
It is increasingly common for data to possess intricate structure, necessitating new models and analytical tools. Graphs, a prominent type of structure, can encode the relationships between any two entities (nodes). However, graphs neither…
A discrete-time totally asymmetric simple exclusion process on a lattice with open boundaries is considered. There are particles of different types. The type of a particle is characterized by the probability that a particle moves to a…
The paper is dealing with semi-classical asymptotics of a characteristic function for a stochastic process. The main technical tool is provided by the stationary phase method. The extremal range for a stochastic process is defined by limit…
The article contains an overview over locally stationary processes. At the beginning time varying autoregressive processes are discussed in detail - both as as a deep example and an important class of locally stationary processes. In the…
In this paper we analyze the approximation of stable linear time-invariant systems, like the Hilbert transform, by sampling series for bandlimited functions in the Paley-Wiener space $\mathcal{PW}_{\pi}^{1}$. It is known that there exist…
In this paper, we propose a low rank approximation method for efficiently solving stochastic partial differential equations. Specifically, our method utilizes a novel low rank approximation of the stiffness matrices, which can significantly…
When only few data samples are accessible, utilizing structural prior knowledge is essential for estimating covariance matrices and their inverses. One prominent example is knowing the covariance matrix to be Toeplitz structured, which…
Methods of estimation and forecasting for stationary models are well known in classical time series analysis. However, stationarity is an idealization which, in practice, can at best hold as an approximation, but for many time series may be…
We consider stationary autoregressive processes with coefficients restricted to an ellipsoid, which includes autoregressive processes with absolutely summable coefficients. We provide consistency results under different norms for the…
Solutions of stationary Fokker-Planck equations in the narrow beam regime are commonly approximated by either ballistic linear transport or by a Fermi pencil-beam equation. We present a rigorous approximation analysis of these three models…
The conditional distribution of the next outcome given the infinite past of a stationary process can be inferred from finite but growing segments of the past. Several schemes are known for constructing pointwise consistent estimates, but…
We propose a novel study of the stochastic proximal gradient method for minimizing the sum of two convex functions, one of which is smooth. Under suitable assumptions and without requiring any boundedness or control of the variance of the…
Comparison to traditionally accurate computing, approximate computing focuses on the rapidity of the satisfactory solution, but not the unnecessary accuracy of the solution. Approximate bisimularity is the approximate one corresponding to…
How to construct a suitable measurement matrix is still an open question in compressed sensing. A significant part of the recent work is that the measurement matrices are not completely random on the entries but exhibit considerable…
Inference for mechanistic models is challenging because of nonlinear interactions between model parameters and a lack of identifiability. Here we focus on a specific class of mechanistic models, which we term stable differential equations.…
We present a sublinear query algorithm for outputting a near-optimal low-rank approximation to any positive semidefinite Toeplitz matrix $T \in \mathbb{R}^{d \times d}$. In particular, for any integer rank $k \leq d$ and $\epsilon,\delta >…
The purpose of this paper is to study the approximation of vector valued mappings defined on a subset of a normed space. We investigate Korovkin-type conditions under which a given sequence of linear operators becomes a so-called…