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Dr Conrado Da Costa's Outputs (10)

Gaussian, stable, tempered stable and mixed limit laws for random walks in cooling random environments (2025)
Journal Article
Avena, L., Da Costa, C., & Peterson, J. (2025). Gaussian, stable, tempered stable and mixed limit laws for random walks in cooling random environments. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 61(2), 850-889. https://doi.org/10.1214/23-AIHP1450

Random Walks in Cooling Random Environments (RWCRE) is a model of random walks in dynamic random environments where the entire environment is resampled along a fixed sequence of times, called the "cooling sequence", and is kept fixed in between those... Read More about Gaussian, stable, tempered stable and mixed limit laws for random walks in cooling random environments.

Gradual convergence for Langevin dynamics on a degenerate potential (2025)
Journal Article
Barrera, G., da-Costa, C., & Jara, M. (2025). Gradual convergence for Langevin dynamics on a degenerate potential. Stochastic Processes and their Applications, 184, Article 104601. https://doi.org/10.1016/j.spa.2025.104601

In this paper, we study an ordinary differential equation with a degenerate global attractor at the origin, to which we add a white noise with a small parameter that regulates its intensity. Under general conditions, for any fixed intensity, as time... Read More about Gradual convergence for Langevin dynamics on a degenerate potential.

Superdiffusive planar random walks with polynomial space–time drifts (2024)
Journal Article
da Costa, C., Menshikov, M., Shcherbakov, V., & Wade, A. (2024). Superdiffusive planar random walks with polynomial space–time drifts. Stochastic Processes and their Applications, 176, Article 104420. https://doi.org/10.1016/j.spa.2024.104420

We quantify superdiffusive transience for a two-dimensional random walk in which the vertical coordinate is a martingale and the horizontal coordinate has a positive drift that is a polynomial function of the individual coordinates... Read More about Superdiffusive planar random walks with polynomial space–time drifts.

Stochastic billiards with Markovian reflections in generalized parabolic domains (2023)
Journal Article
da Costa, C., Menshikov, M. V., & Wade, A. R. (2023). Stochastic billiards with Markovian reflections in generalized parabolic domains. Annals of Applied Probability, 33(6B), 5459-5496. https://doi.org/10.1214/23-AAP1952

We study recurrence and transience for a particle that moves at constant velocity in the interior of an unbounded planar domain, with random reflections at the boundary governed by a Markov kernel producing outgoing angles from incoming angles. Our d... Read More about Stochastic billiards with Markovian reflections in generalized parabolic domains.

Laws of Large Numbers for Weighted Sums of Independent Random Variables: A Game of Mass (2023)
Journal Article
Avena, L., & da Costa, C. (2024). Laws of Large Numbers for Weighted Sums of Independent Random Variables: A Game of Mass. Journal of Theoretical Probability, 37(1), 81-120. https://doi.org/10.1007/s10959-023-01296-z

We consider weighted sums of independent random variables regulated by an increment sequence and provide operative conditions that ensure a strong law of large numbers for such sums in both the centred and non-centred case. The existing criteria for... Read More about Laws of Large Numbers for Weighted Sums of Independent Random Variables: A Game of Mass.

Reaction–Diffusion Models for a Class of Infinite-Dimensional Nonlinear Stochastic Differential Equations (2022)
Journal Article
da Costa, C., Freitas Paulo da Costa, B., & Valesin, D. (2023). Reaction–Diffusion Models for a Class of Infinite-Dimensional Nonlinear Stochastic Differential Equations. Journal of Theoretical Probability, 36, 1059–1087. https://doi.org/10.1007/s10959-022-01187-9

We establish the existence of solutions to a class of nonlinear stochastic differential equations of reaction–diffusion type in an infinite-dimensional space, with diffusion corresponding to a given transition kernel. The solution obtained is the sca... Read More about Reaction–Diffusion Models for a Class of Infinite-Dimensional Nonlinear Stochastic Differential Equations.

Random walk in cooling random environment: recurrence versus transience and mixed fluctuations (2022)
Journal Article
Avena, L., Chino, Y., da Costa, C., & den Hollander, F. (2022). Random walk in cooling random environment: recurrence versus transience and mixed fluctuations. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 58(2), 967-1009. https://doi.org/10.1214/21-aihp1184

This is the third in a series of papers in which we consider one-dimensional Random Walk in Cooling Random Environment (RWCRE). The latter is obtained by starting from one-dimensional Random Walk in Random Environment (RWRE) and resampling the enviro... Read More about Random walk in cooling random environment: recurrence versus transience and mixed fluctuations.

Random walk in cooling random environment: ergodic limits and concentration inequalities (2019)
Journal Article
Avena, L., Chino, Y., da Costa, C., & den Hollander, F. (2019). Random walk in cooling random environment: ergodic limits and concentration inequalities. Electronic Journal of Probability, 24, Article 38. https://doi.org/10.1214/19-ejp296

In previous work by Avena and den Hollander [3], a model of a random walk in a dynamic random environment was proposed where the random environment is resampled from a given law along a given sequence of times. In the regime where the increments of t... Read More about Random walk in cooling random environment: ergodic limits and concentration inequalities.