Using the weak convergence approach to large deviations, we formulate and prove deviation principle (LDP) for W-random graphs in cut-norm topology. This generalizes LDP Erd?s–Rényi random by Chatterjee Varadhan. Furthermore, translate a class of interacting dynamical systems on such graphs. To this end, demonstrate that solutions models depend continuously underlying with respect apply contract...

This work addresses some asymptotic behavior of solutions to stochastic convective Brinkman–Forchheimer (SCBF) equations perturbed by multiplicative Gaussian noise in two and three dimensional bounded domains. Using a weak convergence approach Budhiraja Dupuis, we establish the Laplace principle for strong solution SCBF suitable Polish space. Then, Wentzell–Freidlin type large deviation is deri...

Abstract Stochastic processes with random reinforced relocations have been introduced in a series of papers by Boyer and co-authors (Boyer Solis Salas 2014, Pineda 2016, Boyer, Evans Majumdar 2017) to model animal foraging behaviour. Such process evolves as Markov process, except at relocation times, when it chooses time its whole past according some ‘memory kernel’, jumps value that time. We p...