Related papers: Policy with stochastic hysteresis
In this paper, we learn dynamics models for parametrized families of dynamical systems with varying properties. The dynamics models are formulated as stochastic processes conditioned on a latent context variable which is inferred from…
We consider a sequential decision making process, such as renewable energy trading or electrical production scheduling, whose outcome depends on the future realization of a random factor, such as a meteorological variable. We assume that…
Stochastic reduced-order models are widely used to represent the effective dynamics of complex systems, but estimating their drift and diffusion coefficients from data remains challenging. Standard approaches often rely on short-time…
We develop methods for estimating how infinitesimal policy changes affect long-term outcomes in dynamic systems. We show that dynamic marginal policy effects (MPEs) can be identified via tractable reduced-form expressions, and can be…
Recently a path integral formalism has been proposed by the author which gives the time evolution of moments of slow variables in a Hamiltonian statistical system. This closure relies on evaluating the informational discrepancy of a time…
In this chapter we review stochastic modelling methods in climate science. First we provide a conceptual framework for stochastic modelling of deterministic dynamical systems based on the Mori-Zwanzig formalism. The Mori-Zwanzig equations…
Statistical thermodynamics delivers the probability distribution of the equilibrium state of matter through the constrained maximization of a special functional, entropy. Its elegance and enormous success have led to numerous attempts to…
This paper studies an optimal control problem for continuous-time stochastic systems subject to reachability objectives specified in a subclass of metric interval temporal logic specifications, a temporal logic with real-time constraints.…
Understanding the spatial extent of extreme precipitation is necessary for determining flood risk and adequately designing infrastructure (e.g., stormwater pipes) to withstand such hazards. While environmental phenomena typically exhibit…
Increasingly larger data sets of processes in space and time ask for statistical models and methods that can cope with such data. We show that the solution of a stochastic advection-diffusion partial differential equation provides a…
Finding the optimal policy for multi-period perishable inventory systems requires solving computationally-expensive stochastic dynamic programs (DP). To avoid the difficulty of solving DP models, we propose a framework that uses an…
We show that a substantial portion of stochastic calculus can be developed along similar lines to ordinary calculus, with derivative-based concepts driving the development. We define a notion of stopping derivative, which is a form of right…
This paper develops a mathematical framework for the analysis of continuous-time trading strategies which, in contrast to the classical setting of continuous-time mathematical finance, does not rely on stochastic integrals or other…
In multi-period stochastic optimization problems, the future optimal decision is a random variable whose distribution depends on the parameters of the optimization problem. We analyze how the expected value of this random variable changes…
A new stochastic theory of a foreign exchange markets dynamics is developed. As a result we have the new probability distribution which well describes statistical and scaling dependencies ''experimentally'' observed in foreign exchange…
In machine learning and computer vision, optimal transport has had significant success in learning generative models and defining metric distances between structured and stochastic data objects, that can be cast as probability measures. The…
Stochastic methods are a crucial area in contemporary climate research and are increasingly being used in comprehensive weather and climate prediction models as well as reduced order climate models. Stochastic methods are used as…
Extinction of an epidemic or a species is a rare event that occurs due to a large, rare stochastic fluctuation. Although the extinction process is dynamically unstable, it follows an optimal path that maximizes the probability of…
Recently path integral methods have been developed for stochastic optimal control for a wide class of models with non-linear dynamics in continuous space-time. Path integral methods find the control that minimizes the expected cost-to-go.…
Trajectory optimization is a fundamental stochastic optimal control problem. This paper deals with a trajectory optimization approach for dynamical systems subject to measurement noise that can be fitted into linear time-varying stochastic…