Related papers: Wavelet-based simulation of random processes from …
Consider $n$ independent Goldstein-Kac telegraph processes $X_1(t), \dots ,X_n(t), \; n\ge 2, \; t\ge 0,$ on the real line $\Bbb R$. Each the process $X_k(t), \; k=1,\dots,n,$ describes a stochastic motion at constant finite speed $c_k>0$…
Suppose we observe a trajectory of length $n$ from an exponentially $\alpha$-mixing stochastic process over a finite but potentially large state space. We consider the problem of estimating the probability mass placed by the stationary…
This work is intended as a contribution to a wavelet-based adaptive estimator of the memory parameter in the classical semi-parametric framework for Gaussian stationary processes. In particular we introduce and develop the choice of a…
Gaussian process (GP) priors are non-parametric generative models with appealing modelling properties for Bayesian inference: they can model non-linear relationships through noisy observations, have closed-form expressions for training and…
A stochastic wavevector approach is formulated to accurately represent compressible turbulence subject to rapid deformations. This approach is inspired by the incompressible particle representation model of Kassinos (1995) and preserves the…
In this paper we introduce a new class of state space models based on shot-noise simulation representations of non-Gaussian L\'evy-driven linear systems, represented as stochastic differential equations. In particular a conditionally…
Generating highly detailed, complex data is a long-standing and frequently considered problem in the machine learning field. However, developing detail-aware generators remains an challenging and open problem. Generative adversarial…
The paper characterizes uniform convergence rate for general classes of wavelet expansions of stationary Gaussian random processes. The convergence in probability is considered.
This paper focuses on estimating the invariant density function $f_X$ of the strongly mixing stationary process $X_t$ in the multiplicative measurement errors model $Y_t = X_t U_t$, where $U_t$ is also a strongly mixing stationary process.…
Many robotic tasks, such as human-robot interactions or the handling of fragile objects, require tight control and limitation of appearing forces and moments alongside sensible motion control to achieve safe yet high-performance operation.…
Discrete-time models are very convenient to simulate a nonlinear system on a computer. In order to build the discrete-time simulation models for the nonlinear feedback systems (which is a very important class of systems in many…
We introduce a nonparametric approach for estimating drift and diffusion functions in systems of stochastic differential equations from observations of the state vector. Gaussian processes are used as flexible models for these functions and…
How to model distribution of sequential data, including but not limited to speech and human motions, is an important ongoing research problem. It has been demonstrated that model capacity can be significantly enhanced by introducing…
We consider a stochastic fluid queue served by a constant rate server and driven by a process which is the local time of a certain Markov process. Such a stochastic system can be used as a model in a priority service system, especially when…
A large amount of observational data has been accumulated in various fields in recent times, and there is a growing need to estimate the generating processes of these data. A linear non-Gaussian acyclic model (LiNGAM) based on the…
We discuss one-dimensional stochastic processes defined through the Temperley-Lieb algebra related to the Q=1 Potts model. For various boundary conditions, we formulate a conjecture relating the probability distribution which describes the…
We present the elliptical processes -- a family of non-parametric probabilistic models that subsumes the Gaussian process and the Student-t process. This generalization includes a range of new fat-tailed behaviors yet retains computational…
For each $\lambda>0$ and every square-integrable infinitely-divisible (ID) distribution there exists at least one stationary stochastic process $t\mapsto X_t$ with the specified distribution for $X_1$ and with first-order autoregressive…
A class of random non-stationary signals termed timbre x dynamics is introduced and studied. These signals are obtained by non-linear transformations of sta-tionary random gaussian signals, in such a way that the transformation can be…
Directional data arise in various contexts such as oceanography (wave directions) and meteorology (wind directions), as well as with measurements on a periodic scale (weekdays, hours, etc.). Our contribution is to introduce a model-based…