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Estimating parameters of a diffusion process given continuous-time observations of the process via maximum likelihood approaches or, online, via stochastic gradient descent or Kalman filter formulations constitutes a well-established…

By employing the technique of enlargement of filtrations, we demonstrate how to incorporate information about the future trend of the stochastic interest rate process into a financial model. By modeling the interest rate as an affine…

Single-particle traces of the diffusive motion of molecules, cells, or animals are by-now routinely measured, similar to stochastic records of stock prices or weather data. Deciphering the stochastic mechanism behind the recorded dynamics…

Energy companies need efficient procedures to perform market calibration of stochastic models for commodities. If the Black framework is chosen for option pricing, the bottleneck of the market calibration is the computation of the variance…

Estimation of high-dimensional covariance matrices in latent factor models is an important topic in many fields and especially in finance. Since the number of financial assets grows while the estimation window length remains of limited…

There are several approaches to modeling and forecasting time series as applied to prices of commodities and financial assets. One of the approaches is to model the price as a non-stationary time series process with heteroscedastic…

Conditional diffusion models provide a natural framework for probabilistic prediction of dynamical systems and have been successfully applied to fluid dynamics and weather prediction. However, in many settings, the available information at…

Stochastic volatility models are the backbone of financial engineering. We study both continuous time diffusions as well as discrete time models. We propose two novel approaches to estimating stochastic volatility diffusions, one using…

In the analysis of commodity futures, it is commonly assumed that futures prices are driven by two latent factors: short-term fluctuations and long-term equilibrium price levels. In this study, we extend this framework by introducing a…

We describe the mathematical theory of diffusion and heat transport with a view to including some of the main directions of recent research. The linear heat equation is the basic mathematical model that has been thoroughly studied in the…

This paper investigates the problem of distributed stochastic approximation in multi-agent systems. The algorithm under study consists of two steps: a local stochastic approximation step and a diffusion step which drives the network to a…

This paper examines the problem of pricing spread options under some models with jumps driven by Compound Poisson Processes and stochastic volatilities in the form of Cox-Ingersoll-Ross(CIR) processes. We derive the characteristic function…

This paper proposes a novel diffusion-index model for forecasting when predictors are high-dimensional matrix-valued time series. We apply an $\alpha$-PCA method to extract low-dimensional matrix factors and build a bilinear regression…

This paper studies high-dimensional curve time series with common stochastic trends. A dual functional factor model structure is adopted with a high-dimensional factor model for the observed curve time series and a low-dimensional factor…

We propose Diffusion-Informed Model Predictive Control (D-I MPC), a generic framework for uncertainty-aware prediction and decision-making in partially observable stochastic systems by integrating diffusion-based time series forecasting…

Forecasting future weather and climate is inherently difficult. Machine learning offers new approaches to increase the accuracy and computational efficiency of forecasts, but current methods are unable to accurately model uncertainty in…

We introduce a \textit{non-modal} analysis technique that characterizes the diffusion properties of spectral element methods for linear convection-diffusion systems. While strictly speaking only valid for linear problems, the analysis is…

Mandatory emission trading schemes are being established around the world. Participants of such market schemes are always exposed to risks. This leads to the creation of an accompanying market for emission-linked derivatives. To evaluate…

Sequential models like recurrent neural networks and transformers have become standard for probabilistic multivariate time series forecasting across various domains. Despite their strengths, they struggle with capturing high-dimensional…

This paper develops an inferential theory for state-varying factor models of large dimensions. Unlike constant factor models, loadings are general functions of some recurrent state process. We develop an estimator for the latent factors and…