**Objective:**

The main goal of this project is the formulation of a stochastic dynamic prediction theory for ensemble forecasting of wildfire propagation.
In spite of the fact that ensemble forecasting is a successful technique in weather prediction, its formulation for wildfire propagation is not at all a merely application in another field of an already existing technique. In fact, although the idea of ensemble forecasting is meaningful for wildfire propagation because it is a nonlinear and chaotic system as well as the weather system is, we stress that in the case of wildfires the stochastic dynamics refers to the evolution of a surface rather than to the evolution of a dynamical observable. Hence, in this sense, the formulation of a stochastic dynamic prediction theory for ensemble forecasting of wildfire propagation mainly consists in the development from scratch of a stochastic process for geometrical figures. This new mathematical object is not embodied by a stochastic process developed on a manifold (at least with boundary), but indeed it is embodied by a stochastic process developed for the edge itself of the manifold. This is the main novel contribution from this project to the advancement of Mathematics. Because of its pioneering character, this will be developed for the simplest manifold with boundary: that is the ellipse, but at the same time this simple manifold is exactly what we need, in first approximation, for modelling wildfire propagation.
The stochastic dynamic theory will be formulated after the derivation, from a reaction-diffusion equation, of a Lorenz-type chaotic system for wildfires: this derivation is a novelty, too. The models' performance is improved by incorporating data through data-assimilation techniques. Moreover, since fire spread models have a spatial character, they are perfectly suitable for being integrated in a Geographic Information System (GIS). This holds true for the input data as well as for the representation of the models' outputs. From this, it follows that GIS applications are the proper tools also for the representation of the estimated probability maps. At the end, this project will be the first study of this sort so far completed. Apart from social, environmental and economical positive impacts due to the improvement of the predictions, the research leads to a technological breakthrough, namely to a probabilistic adjustment of real-time estimation of wildfire perimeters when this estimation is based on crowdsourcing, e.g., through web-blog, twitter, WhatsApp .... In fact, the accuracy of crowdsourced data cannot be increased by itself, but the inaccuracy of such real-time data can be dealt in the same manner as the uncertainty in the initial state of the fire is dealt by the stochastic dynamic theory herein formulated.