相关论文: Differentiating sigma-fields for Gaussian and shif…
The paper investigates uniform convergence of wavelet expansions of Gaussian random processes. The convergence is obtained under simple general conditions on processes and wavelets which can be easily verified. Applications of the developed…
In this paper, we introduce and study McKean-Vlasov processes of bridge type. Specifically, we examine a stochastic differential equation (SDE) of the form: $$\mathrm{d} \xi_t=-\mu(t,\mathbb{E}[\varphi_1(\xi_t)]) \frac{\xi_t}{T-t}…
In this paper we study a stochastic differential equation driven by a fractional Brownian motion with a discontinuous coefficient. We also give an approximation to the solution of the equation. This is a first step to define a fractional…
Gaussian processes are arguably the most important class of spatiotemporal models within machine learning. They encode prior information about the modeled function and can be used for exact or approximate Bayesian learning. In many…
In this paper, we present a new approach to derive series expansions for some Gaussian processes based on harmonic analysis of their covariance function. In particular, we propose a new simple rate-optimal series expansion for fractional…
We first state a special type of It\^o formula involving stochastic integrals of both standard and fractional Brownian motions. Then we use Doss-Sussman transformation to establish the link between backward doubly stochastic differential…
Many complex systems are characterized by intriguing spatio-temporal structures. Their mathematical description relies on the analysis of appropriate correlation functions. Functional integral techniques provide a unifying formalism that…
Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…
We analyze in a closed form the learning dynamics of stochastic gradient descent (SGD) for a single-layer neural network classifying a high-dimensional Gaussian mixture where each cluster is assigned one of two labels. This problem provides…
We study a nonparametric Bayesian approach to estimation of the volatility function of a stochastic differential equation driven by a gamma process. The volatility function is modelled a priori as piecewise constant, and we specify a gamma…
The description of invariants of surfaces with respect to the motion groups is reduced to the description of invariants of parameterized surfaces with respect to the motion groups. Existence of a commuting system of invariant partial…
A recurrent theme in functional analysis is the interplay between the theory of positive definite functions, and their reproducing kernels, on the one hand, and Gaussian stochastic processes, on the other. This central theme is motivated by…
In this article we prove large deviations principles for high minima of Gaussian processes with nonnegatively correlated increments on arbitrary intervals. Furthermore, we prove large deviations principles for the increments of such…
Bayesian field theory denotes a nonparametric Bayesian approach for learning functions from observational data. Based on the principles of Bayesian statistics, a particular Bayesian field theory is defined by combining two models: a…
Complex-valued Gaussian processes are used in Bayesian frequency-domain system identification as prior models for regression. If each realization of such a process were an $H_\infty$ function with probability one, then the same model could…
Invariant foliations are complicated random sets useful for describing and understanding the qualitative behaviors of nonlinear dynamical systems. We will consider invariant foliations for stochastic partial differential equation with…
Motivated by problems from statistical analysis for discretely sampled SPDEs, first we derive central limit theorems for higher order finite differences applied to stochastic process with arbitrary finitely regular paths. These results are…
Gaussian random fields pervade all areas of science. However, it is often the departures from Gaussianity that carry the crucial signature of the nonlinear mechanisms at the heart of diverse phenomena, ranging from structure formation in…
We introduce the class of vector measures of bounded $\gamma$-variation and study its relationship with vector-valued stochastic integrals with respect to Brownian motions.
Stochastic processes on manifolds over non-Archimedean fields and with transition measures having values in the field $\bf C$ of complex numbers are defined and investigated. The analogs of Markov, Poisson and Wiener processes are studied.…