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Conceptual delay models have played a key role in the understanding of El Ni\~no-Southern Oscillation (ENSO) variability. Based on such delay models, we propose a novel scenario for the fabric of ENSO variability resulting from the subtle…
This paper deals with a consistent estimator of the multifunction involved in a time-discretized Skorokhod reflection problem defined by a stochastic differential equation and a Moreau sweeping process.
We develop an eigenvalue-based approach for the stability assessment and stabilization of linear systems with multiple delays and periodic coefficient matrices. Delays and period are assumed commensurate numbers, such that the Floquet…
We develop a class of pathwise inequalities of the form $H(B_t)\ge M_t+F(L_t)$, where $B_t$ is Brownian motion, $L_t$ its local time at zero and $M_t$ a local martingale. The concrete nature of the representation makes the inequality useful…
We show an intimate connection between solutions of the Skorokhod Embedding Problem which are given as the first hitting time of a barrier and the concept of shadows in martingale optimal transport. More precisely, we show that a solution…
We derive the optimal rate of convergence for the mean squared error at the terminal point for anticipating linear stochastic differential equations, where the integral is interpreted in Skorohod sense. Although alternative proof techniques…
This paper proposes a supervisory control structure for networked systems with time-varying delays. The control structure, in which a supervisor triggers the most appropriate controller from a multi-controller unit, aims at improving the…
Delays are ubiquitous in applied problems, but often do not arise as the simple constant discrete delays that analysts and numerical analysts like to treat. In this chapter we show how state-dependent delays arise naturally when modeling…
Decentralized stochastic control problems involving general state/measurement/action spaces are intrinsically difficult to study because of the inapplicability of standard tools from centralized (single-agent) stochastic control. In this…
The Skorokhod map on the half-line has proved to be a useful tool for studying processes with non-negativity constraints. In this work we introduce a measure-valued analog of this map that transforms each element $\zeta$ of a certain class…
In this paper, we address the stochastic representation problem in discrete time under (non-linear) g-expectation. We establish existence and uniqueness of the solution, as well as a characterization of the solution. As an application, we…
In order to approximate a continuous time stochastic process by discrete time Markov chains one has several options to embed the Markov chains into continuous time processes. On the one hand there is the Markov embedding, which uses…
Sequential filtering and spatial inverse problems assimilate data points distributed either temporally (in the case of filtering) or spatially (in the case of spatial inverse problems). Sometimes it is possible to choose the position of…
Structured embedding transformations offer a promising approach for enhancing the efficiency and coherence of language model inference. The introduction of Structural Embedding Projection (SEP) provides a mechanism for refining token…
A general and new stochastic linear quadratic optimal control problem is studied, where the coefficients are allowed to be time-varying, and both state delay and control delay can appear simultaneously in the state equation and the cost…
We are interested in privatizing an approximate posterior inference algorithm called Expectation Propagation (EP). EP approximates the posterior by iteratively refining approximations to the local likelihoods, and is known to provide better…
The spectral deferred correction (SDC) method is class of iterative solvers for ordinary differential equations (ODEs). It can be interpreted as a preconditioned Picard iteration for the collocation problem. The convergence of this method…
This work focuses on the well-posedness of abstract stochastic linear systems with boundary input delay and unbounded observation operators. We use product spaces and a semigroup approach to reformulate such delay systems into free-delay…
We study the impact of competing time delays in coupled stochastic synchronization and coordination problems. We consider two types of delays: transmission delays between interacting elements and processing, cognitive, or execution delays…
We analyze the convergence of gradient-based optimization algorithms that base their updates on delayed stochastic gradient information. The main application of our results is to the development of gradient-based distributed optimization…