• tipping points
• climate change
• early warning indicators
• SDE
• SPDE

The main purpose of this thesis is to carry out a mathematical analysis of tipping points in the climatic field using low-dimensional stochastic models. Specific attention is given to the problem of identifying proximity indicators to a critical point using time series indicators. In particular, in the first part of this work we study and simulate three 0-dimensional models related to climate presenting a tipping point. The two first models considered are made up by a stochastic differential equation characterized by bistability or the presence of a bifurcation. Next to these, the third model considered is a more realistic climatic model for Earth vegetation-climate interaction. Finally, the second part of the thesis is dedicated to the study of a simplified energy balance model given by a stochastic partial differential equation. Briefly, we study the problem of existence and uniqueness using an integral formulation and semigroup theory. In addition, we investigate numerically the transitions between stable states in dimension 1.