Related papers: Stochastic differential theory of cricket
This paper proposes a methodology to estimate characteristic functions of stochastic differential equations that are defined over polynomials and driven by L\'evy noise. For such systems, the time evolution of the characteristic function is…
Technology has had an unquestionable impact on the way people watch sports. Along with this technological evolution has come a higher standard to ensure a good viewing experience for the casual sports fan. It can be argued that the…
In this second part of our two-part paper, we invoke the stochastic maximum principle, conditional Hamiltonian and the coupled backward-forward stochastic differential equations of the first part [1] to derive team optimal decentralized…
We investigated the temporal distribution of goals in soccer using event-level data from 3,433 matches across 21 leagues and competitions. Contrary to the prevailing notion of randomness, we found that the probability of a goal being scored…
We propose a general stochastic formalism for describing the evolution of chemical reactions involving a finite number of molecules. This approach is consistent with the statistical analysis based on the Chemical Master Equation, and…
Stochastic games combine controllable and adversarial non-determinism with stochastic behavior and are a common tool in control, verification and synthesis of reactive systems facing uncertainty. Multi-objective stochastic games are natural…
This review maps developments in stochastic modeling, highlighting non-standard approaches and their applications to biology and epidemiology. It brings together four strands: (1) core models for systems that evolve with randomness; (2)…
It is critical yet challenging for deep learning models to properly characterize uncertainty that is pervasive in real-world environments. Although a lot of efforts have been made, such as heteroscedastic neural networks (HNNs), little work…
The problem of function approximation by neural dynamical systems has typically been approached in a top-down manner: Any continuous function can be approximated to an arbitrary accuracy by a sufficiently complex model with a given…
Defensive forecasting is a method of transforming laws of probability (stated in game-theoretic terms as strategies for Sceptic) into forecasting algorithms. There are two known varieties of defensive forecasting: "continuous", in which…
The main contributions of this paper are three fold. First, our primary concern is to investigate a class of stochastic recursive delayed control problems which arise naturally with sound backgrounds but have not been well-studied yet. For…
In this paper we bring a novel approach to the theory of tournament rankings. We combine two different theories that are widely used to establish rankings of populations after a given tournament. First, we use the statistical approach of…
Stochastic thermodynamics is formulated for variables that are odd under time reversal. The invariance under spatial rotation of the collision rates due to the isotropy of the heat bath is shown to be a crucial ingredient. An alternative…
Technology offers new ways to measure the locations of the players and of the ball in sports. This translates to the trajectories the ball takes on the field as a result of the tactics the team applies. The challenge professionals in soccer…
The evolution of digital technology and the increasing popularity of sports inspired the innovators to take the experience of users with a proclivity towards sports to a whole new different level, by introducing Fantasy Sports Platforms…
Stochastic differential equations (SDEs) are of utmost importance in various scientific and industrial areas. They are the natural description of dynamical processes whose precise equations of motion are either not known or too expensive to…
This paper considers a stochastic approximation algorithm, with decreasing step size and martingale difference noise. Under very mild assumptions, we prove the non convergence of this process toward a certain class of repulsive sets for the…
We discuss the general framework of a stochastic two-player, hybrid differential game, and we apply it to the modelling of a "match race" between two sailing boats, namely a competition in which the goal of both players is to proceed in the…
Statistical learning theory is the foundation of machine learning, providing theoretical bounds for the risk of models learned from a (single) training set, assumed to issue from an unknown probability distribution. In actual deployment,…
Neural Stochastic Differential Equations (NSDEs) model the drift and diffusion functions of a stochastic process as neural networks. While NSDEs are known to make accurate predictions, their uncertainty quantification properties have been…