Active systems evade the rules of equilibrium thermodynamics by constantly dissipating
energy at the level of their microscopic components. This energy flux stems from the …

The theory of large deviations is concerned with the exponential decay of probabilities of
large fluctuations in random systems. These probabilities are important in many fields of …

In deep latent Gaussian models, the latent variable is generated by a time-inhomogeneous
Markov chain, where at each time step we pass the current state through a parametric …

Concentration inequalities deal with deviations of functions of independent random
variables from their expectation. In the last decade new tools have been introduced making …

This book is concerned with the study of the probabilities of very rare events. To understand
why rare events are important at all, one only has to think of a lottery to be convinced that …

Hidden Markov models—most often abbreviated to the acronym “HMMs”—are one of the
most successful statistical modelling ideas that have came up in the last forty years: the use …

The original work in recursive stochastic algorithms was by Robbins and Monro, who
developed and analyzed a recursive procedure for finding the root of a real-valued function …

This book is an introduction to optimal stochastic control for continuous time Markov
processes and the theory of viscosity solutions. It covers dynamic programming for …

We propose and characterize a model of preferences over acts such that the decision maker
prefers act f to act g if and only if 𝔼μφ (𝔼πu○ f) 𝔼μφ (𝔼πu○ g), where 𝔼 is the expectation …

The standard theory of decision making under uncertainty advises the decision maker to
form a statistical model linking outcomes to decisions and then to choose the optimal …