相关论文: Operator Methods, Abelian Processes and Dynamic Co…

A stochastic procedure is developed which allows one to express Pontryagin's maximum principle for dissipative quantum system solely in terms of stochastic wave functions. Time-optimal controls can be efficiently computed without computing…

We study existence and uniqueness of the fixed points solutions of a large class of non-linear variable discounted transfer operators associated to a sequential decision-making process. We establish regularity properties of these solutions,…

When considering the problem of forecasting a continuous-time stochastic process over an entire time-interval in terms of its recent past, the notion of Autoregressive Hilbert space processes (ARH) arises. This model can be seen as a…

This thesis is devoted to the study of affine processes and their applications in financial mathematics. In the first part we consider the theory of time-inhomogeneous affine processes on general state spaces. We present a concise setup for…

We consider asset price models whose dynamics are described by linear functions of the (time extended) signature of a primary underlying process, which can range from a (market-inferred) Brownian motion to a general multidimensional…

Data assimilation is the task of combining mathematical models with observational data. From a mathematical perspective data assimilation leads to Bayesian inference problems which can be formulated in terms of Feynman-Kac formulae. In this…

For deterministic and probabilistic programs we investigate the problem of program synthesis and program optimisation (with respect to non-functional properties) in the general setting of global optimisation. This approach is based on the…

We present a flexible data-driven method for dynamical system analysis that does not require explicit model discovery. The method is rooted in well-established techniques for approximating the Koopman operator from data and is implemented…

The recent experimental progresses in handling microscopic systems have allowed to probe them at levels where fluctuations are prominent, calling for stochastic modeling in a large number of physical, chemical and biological phenomena. This…

Markov Decision Processes (MDPs) are a formal framework for modeling and solving sequential decision-making problems. In finite-time horizons such problems are relevant for instance for optimal stopping or specific supply chain problems,…

In this paper we consider a broad class of infinite horizon discrete-time optimal control models that involve a nonnegative cost function and an affine mapping in their dynamic programming equation. They include as special cases classical…

Markov models are often used to capture the temporal patterns of sequential data for statistical learning applications. While the Hidden Markov modeling-based learning mechanisms are well studied in literature, we analyze a…

Hebbian learning theory is rooted in Pavlov's Classical Conditioning. While mathematical models of the former have been proposed and studied in the past decades, especially in spin glass theory, only recently it has been numerically shown…

The success of quantum physics in description of various physical interaction phenomena relies primarily on the accuracy of analytical methods used. In quantum mechanics, many of such interactions such as those found in quantum…

We introduce a framework for approximate dynamic programming that we apply to discrete time chains on $\mathbb{Z}_+^d$ with countable action sets. Our approach is grounded in the approximation of the (controlled) chain's generator by that…

We develop a stochastic volatility framework for modeling multiple currencies based on CBI-time-changed L\'evy processes. The proposed framework captures the typical risk characteristics of FX markets and is coherent with the symmetries of…

The main goal of this paper is to apply the machinery of variational analysis and generalized differentiation to study infinite horizon stochastic dynamic programming (DP) with discrete time in the Banach space setting without convexity…

Active classification, i.e., the sequential decision-making process aimed at data acquisition for classification purposes, arises naturally in many applications, including medical diagnosis, intrusion detection, and object tracking. In this…

The thermodynamic formalism allows one to access the chaotic properties of equilibrium and out-of-equilibrium systems, by deriving those from a dynamical partition function. The definition that has been given for this partition function…

In this article, we present an extension of the formulation recently developed by the authors (A Framework for Data-Driven Computational Mechanics Based on Nonlinear Optimization, arXiv:1910.12736 [math.NA]) to the structural dynamics…