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Filtering and parameter estimation under partial information for multiscale problems is studied in this paper. After proving mean square convergence of the nonlinear filter to a filter of reduced dimension, we establish that the conditional…
We focus on estimating the integrated covariance of log-price processes in the presence of market microstructure noise. We construct an efficient unbiased estimator for the quadratic covariation of two It\^{o} processes in the case where…
We conducted an extensive computational experiment, lasting multiple CPU-years, to optimally select parameters for two important classes of algorithms for finding sparse solutions of underdetermined systems of linear equations. We make the…
We propose a provably stabilizing and tractable approach for control of constrained linear systems under intermittent observations and unreliable transmissions of control commands. A smart sensor equipped with a Kalman filter is employed…
Stochastic approximation is a framework unifying many random iterative algorithms occurring in a diverse range of applications. The stability of the process is often difficult to verify in practical applications and the process may even be…
We treat the optimal linear filtering problem for a sum of two second order uncorrelated generalized stochastic processes. This is an operator equation involving covariance operators. We study both the wide-sense stationary case and the…
Instrumental variable methods are often used for parameter estimation in the presence of confounding. They can also be applied in stochastic processes. Instrumental variable analysis exploits moment equations to obtain estimators for causal…
This paper investigates the parareal algorithms for solving the stochastic Maxwell equations driven by multiplicative noise, focusing on their convergence, computational efficiency and numerical performance. The algorithms use the…
Time-dependent correlation functions of (unstable) particles undergoing biased or unbiased diffusion, coagulation and annihilation are calculated. This is achieved by similarity transformations between different stochastic models and…
The dynamics of cellular chemical reactions are variable due to stochastic noise from intrinsic and extrinsic sources. The intrinsic noise is the intracellular fluctuations of molecular copy numbers caused by the probabilistic encounter of…
In this work, we explore a time-fractional diffusion equation of order $\alpha \in (0,1)$ with a stochastic diffusivity parameter. We focus on efficient estimation of the expected values (considered as an infinite dimensional integral on…
Parareal is a well-studied algorithm for numerically integrating systems of time-dependent differential equations by parallelising the temporal domain. Given approximate initial values at each temporal sub-interval, the algorithm locates a…
Stochastic computer simulations enable users to gain new insights into complex physical systems. Optimization is a common problem in this context: users seek to find model inputs that maximize the expected value of an objective function.…
We study efficiency of non-parametric estimation of diffusions (stochastic differential equations driven by Brownian motion) from long stationary trajectories. First, we introduce estimators based on conditional expectation which is…
This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…
We consider a non-linear filtering problem, whereby the signal obeys the stochastic Navier-Stokes equations and is observed through a linear mapping with additive noise. The setup is relevant to data assimilation for numerical weather…
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…
Regularly varying stochastic processes model extreme dependence between process values at different locations and/or time points. For such processes we propose a two-step parameter estimation of the extremogram, when some part of the domain…
This article explores the estimation of parameters and states for linear stochastic systems with deterministic control inputs. It introduces a novel Kalman filtering approach called Kalman Filtering with Correlated Noises Recursive…
The problem of optimal estimation of linear functionals $A {\xi}=\int_{0}^{\infty} a(t)\xi(t)dt$ and $A_T{\xi}=\int_{0}^{T} a(t)\xi(t)dt$ depending on the unknown values of random process $\xi(t)$, $t\in R$, with stationary $n$th increments…