Related papers: Non-parametric Inference for Diffusion Processes: …
We consider the problem of nonparametric estimation of the drift and diffusion coefficients of a Stochastic Differential Equation (SDE), based on $n$ independent replicates $\left\{X_i(t)\::\: t\in [0,1]\right\}_{1 \leq i \leq n}$, observed…
Inferring a diffusion equation from discretely-observed measurements is a statistical challenge of significant importance in a variety of fields, from single-molecule tracking in biophysical systems to modeling financial instruments.…
This paper obtains asymptotic results for parametric inference using prediction-based estimating functions when the data are high frequency observations of a diffusion process with an infinite time horizon. Specifically, the data are…
Diffusion models, which convert noise into new data instances by learning to reverse a diffusion process, have become a cornerstone in contemporary generative modeling. In this work, we develop non-asymptotic convergence theory for a…
We consider the problem of parameter estimation in the case of observation of the trajectory of diffusion process. We suppose that the drift coefficient has a singularity of cusp-type and the unknown parameter corresponds to the position of…
In recent years, we have seen a handful of work on inference algorithms over non-stationary data streams. Given their flexibility, Bayesian non-parametric models are a good candidate for these scenarios. However, reliable streaming…
A scheme is developed for estimating state-dependent drift and diffusion coefficients in a stochastic differential equation from time-series data. The scheme does not require to specify parametric forms for the drift and diffusion…
We propose a new semiparametric approach for modelling nonlinear univariate diffusions, where the observed process is a nonparametric transformation of an underlying parametric diffusion (UPD). This modelling strategy yields a general class…
We consider inference of the parameters of the diffusion term for Cox-Ingersoll-Ross and similar processes with a power type dependence of the diffusion coefficient from the underlying process. We suggest some original pathwise estimates…
This paper gives a brief overview on the nonparametric techniques that are useful for financial econometric problems. The problems include estimation and inferences of instantaneous returns and volatility functions of time-homogeneous and…
Consider a scalar reflected diffusion $(X_t:t\geq 0)$, where the unknown drift function $b$ is modelled nonparametrically. We show that in the low frequency sampling case, when the sample consists of $(X_0,X_\Delta,...,X_{n\Delta})$ for…
Diffusion models, which convert noise into new data instances by learning to reverse a Markov diffusion process, have become a cornerstone in contemporary generative modeling. While their practical power has now been widely recognized, the…
When partitioning workflows in realistic scenarios, the knowledge of the processing units is often vague or unknown. A naive approach to addressing this issue is to perform many controlled experiments for different workloads, each…
In this paper we propose the first non-parametric Bayesian model using Gaussian Processes to make inference on Poisson Point Processes without resorting to gridding the domain or to introducing latent thinning points. Unlike competing…
We study supervised multiclass classification for diffusion processes, where each class is characterized by a distinct drift function and trajectories are observed at discrete times. We first derive a multidimensional Bayes rule and then…
We consider nonlinear partial differential equations (PDEs) for advection-diffusion processes which are augmented by an auxiliary parameter $\delta$ such that $\delta=0$ corresponds to linear advection-diffusion. We derive potentially…
This paper presents a methodology for creating streaming, distributed inference algorithms for Bayesian nonparametric (BNP) models. In the proposed framework, processing nodes receive a sequence of data minibatches, compute a variational…
We consider parametric estimation and tests for multi-dimensional diffusion processes with a small dispersion parameter $\varepsilon$ from discrete observations. For parametric estimation of diffusion processes, the main target is to…
Jump diffusion processes are widely used to model asset prices over time, mainly for their ability to capture complex discontinuous behavior, but inference on the model parameters remains a challenge. Here our goal is posterior inference on…
We consider continuous-time diffusion models driven by fractional Brownian motion. Observations are assumed to possess a non-trivial likelihood given the latent path. Due to the non-Markovianity and high-dimensionality of the latent paths,…