2 citations · 3 across the 7 of their papers we have counts for
7 papers
Large Deviations and the Peano Phenomenon in Stochastic Differential Equations with Homogeneous Drift
Paola Bermolen, Valeria Goicoechea, José R. León
We consider a diffusion equation in with drift equal to the gradient of a homogeneous potential of degree , with , and local variance equal to $\varepsil…
On the number of roots of Sturm-Liouville random sums
Federico Dalmao, José R. León
We consider the number of roots of linear combinations of a system of orthogonal eigenfunctions of a Sturm-Liouville initial value problem with i.i.d. standard Gaussian coeffic…
On a general Kac-Rice formula for the measure of a level set
Diego Armentano, Jean-Marc Azaïs, José Rafael León
Let be a random field , . We first studied the level set , . In particular we gave a weak condi…
Small-time approximation of the transition density for diffusions with singularities. Application to the Wright-Fisher model
Tania Roa, María Inés Fariello, Gerardo Martínez +1
The Wright-Fisher (W-F) diffusion model serves as a foundational framework for interpreting population evolution through allele frequency dynamics over time. Despite the known tran…
Kac-Rice formula: A contemporary overview of the main results and applications
Corinne Berzin, Alain Latour, José León
The book develops the fundamental ideas of the famous Kac-Rice formula for vectorvalued random fields. This formula allows to compute the expectation and moments of the measure, an…
A probabilistic point of view for the Kolmogorov hypoelliptic equations
Pierre Etoré, Jose R León, Clémentine Prieur
In this work, we propose a method for solving Kolmogorov hypoelliptic equations based on Fourier transform and Feynman-Kac formula. We first explain how the Feynman-Kac formula can…
Studying the winding number for stationary Gaussian processes using real variables
Jean-Marc Azaïs, Federico Dalmao, José R. León
We consider the winding number of planar stationary Gaussian processes defined on the line. Under mild conditions, we obtain the asymptotic variance and the Central Limit Theorem f…