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A Two-Stage approach enables researchers to make optimal non-linear predictions via Generalized Ridge Regression using models that contain two or more x-predictor variables and make only realistic minimal assumptions. The optimal regression…
The paper provides an overview of the theory and applications of risk-sensitive Markov decision processes. The term 'risk-sensitive' refers here to the use of the Optimized Certainty Equivalent as a means to measure expectation and risk.…
A theory of Ruelle-Pollicott (RP) resonances for stochastic differential systems is presented. These resonances are defined as the eigenvalues of the generator (Kolmogorov operator) of a given stochastic system. By relying on the theory of…
Semi-Markov processes play an important role in the effective description of partially accessible systems in stochastic thermodynamics. They occur, for instance, in coarse-graining procedures such as state lumping and when analyzing waiting…
An algorithm is presented which generates pairs of oscillatory random time series which have identical periodograms but differ in the number of oscillations. This result indicate the intrinsic limitations of spectral methods when it comes…
Optimal measurements for quantum multiparameter estimation are complicated by the uncertainty principle. Generally, there is a trade-off between the precision with which different parameters can be simultaneously estimated. The task of…
The problem of mean-square optimal linear estimation of linear functionals which depend on the unknown values of a multidimensional stationary stochastic sequence from observations of the sequence with a noise and missing observations is…
The idea of iterative process optimization based on collected output measurements, or "real-time optimization" (RTO), has gained much prominence in recent decades, with many RTO algorithms being proposed, researched, and developed. While…
The Robust Satisficing (RS) model is an emerging approach to robust optimization, offering streamlined procedures and robust generalization across various applications. However, the statistical theory of RS remains unexplored in the…
In this paper, we report stochastic resonance (SR) in a single electron turnstile. It has been known that SR emerges by the cooperation of a weak periodic signal and noise in a bistable system. A periodic signal produces switching between…
The problem of the mean-square optimal estimation of the linear functionals which depend on the unknown values of a stochastic stationary sequence from observations of the sequence in special sets of points is considered. Formulas for…
We analyze the physics of optimal protocols to prepare a target state with high fidelity in a symmetrically coupled two-qubit system. By varying the protocol duration, we find a discontinuous phase transition, which is characterized by a…
It is notoriously difficult to apply statistical mechanics to generally covariant systems, because the notions of time, energy and equilibrium are seriously modified in this context. We discuss the conditions under which weaker versions of…
A fully discrete finite difference scheme for stochastic reaction-diffusion equations driven by a $1+1$-dimensional white noise is studied. The optimal strong rate of convergence is proved without posing any regularity assumption on the…
We study the problem of sequentially testing whether a given stochastic process is generated by a known Markov chain. Formally, given access to a stream of random variables, we want to quickly determine whether this sequence is a trajectory…
We consider stochastic convex optimization problems where the objective is an expectation over smooth functions. For this setting we suggest a novel gradient estimate that combines two recent mechanism that are related to notion of…
We present a renormalized second-order perturbation theory (rPT2), based on a Kohn-Sham (KS) reference state, for the electron correlation energy that includes the random-phase approximation (RPA), second-order screened exchange (SOSEX),…
We study sequential multiple testing with independent data streams, where the goal is to identify an unknown subset of signals while controlling commonly used error metrics, including generalized familywise rates and false discovery and…
We give computable bounds on the rate of convergence of the transition probabilities to the stationary distribution for a certain class of geometrically ergodic Markov chains. Our results are different from earlier estimates of Meyn and…
The thermodynamic uncertainty relation is a prominent result in stochastic thermodynamics that provides a bound on the fluctuations of any thermodynamic flux, also known as current, in terms of the average rate of entropy production. Such…