Related papers: Discretization of Continuous Time Discrete Scale I…
Recently, a novel system identification method based on invariant subspace theory is introduced, aiming to address the identification problem of continuous-time (CT) linear time-invariant (LTI) systems by combining time-domain and…
Discrete diffusion models have seen a surge of attention with applications on naturally discrete data such as language and graphs. Although discrete-time discrete diffusion has been established for a while, only recently Campbell et al.…
This survey addresses sampling discretization and its connections with other areas of mathematics. The survey concentrates on sampling discretization of norms of elements of finite-dimensional subspaces. We present here known results on…
We develop an estimator for the high-dimensional covariance matrix of a locally stationary process with a smoothly varying trend and use this statistic to derive consistent predictors in non-stationary time series. In contrast to the…
Inverse problems in scientific computing often require optimization over infinite-dimensional Hilbert spaces. A commonly used solver in such settings is stochastic gradient descent (SGD), where gradients are approximated using randomly…
We study the problem of computing the value function from a discretely-observed trajectory of a continuous-time diffusion process. We develop a new class of algorithms based on easily implementable numerical schemes that are compatible with…
We formulate a novel approach to solve a class of stochastic problems, referred to as data-consistent inverse (DCI) problems, which involve the characterization of a probability measure on the parameters of a computational model whose…
We propose a hybrid estimation procedure to estimate global fixed parameters and subject-specific random effects in a mixed fractional Black-Scholes model based on discrete-time observations. Specifically, we consider $N$ independent…
Continuous-time Markov process models of contagions are widely studied, not least because of their utility in predicting the evolution of real-world contagions and in formulating control measures. It is often the case, however, that…
We introduce two new estimators of the bivariate Hurst exponent in the power-law cross-correlations setting -- the cross-periodogram and local $X$-Whittle estimators -- as generalizations of their univariate counterparts. As the…
We present a Bayesian non-parametric way of inferring stochastic differential equations for both regression tasks and continuous-time dynamical modelling. The work has high emphasis on the stochastic part of the differential equation, also…
Application of discrete-time survival methods for continuous-time survival prediction is considered. For this purpose, a scheme for discretization of continuous-time data is proposed by considering the quantiles of the estimated event-time…
This paper introduces the novel class of modulated cyclostationary processes, a class of non-stationary processes exhibiting frequency coupling, and proposes a method of their estimation from repeated trials. Cyclostationary processes also…
The sensor placement problem is a common problem that arises when monitoring correlated phenomena, such as temperature, precipitation, and salinity. Existing approaches to this problem typically formulate it as the maximization of…
In this paper we propose the notion of continuous-time dynamic spectral risk-measure (DSR). Adopting a Poisson random measure setting, we define this class of dynamic coherent risk-measures in terms of certain backward stochastic…
We consider the problem of estimating parameters of stochastic differential equations (SDEs) with discrete-time observations that are either completely or partially observed. The transition density between two observations is generally…
We introduce a lattice random walk discretisation scheme for stochastic differential equations (SDEs) that samples binary or ternary increments at each step, suppressing complex drift and diffusion computations to simple 1 or 2 bit random…
Dynamic state estimation (DSE) is becoming increasingly important for monitoring inverter-dominated power systems. Due to their cascading control structures, inverter-based resources (IBRs) exhibit multi-timescale dynamics, leading to stiff…
Expressions for local discrete variance decay (DVD) rates are directly derived from discrete tracer equations without any assumptions on discrete fluxes of the second moment. Spurious mixing (SM) associated with numerical implementations of…
.Stochastic models based on random diffusivities, such as the diffusing-diffusivity approach, are popular concepts for the description of non-Gaussian diffusion in heterogeneous media. Studies of these models typically focus on the moments…