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math.PR2021★ 4 cited
Lower bounds on the Lyapunov exponents of stochastic differential equations
Jacob Bedrossian, Alex Blumenthal, Sam Punshon-Smith
In this article, we review our recently introduced methods for obtaining strictly positive lower bounds on the top Lyapunov exponent of high-dimensional, stochastic differential eq…
math.PR2021★ 11 cited
On the pitchfork bifurcation for the Chafee-Infante equation with additive noise
Alex Blumenthal, Maximilian Engel, Alexandra Neamtu
We investigate pitchfork bifurcations for a stochastic reaction diffusion equation perturbed by an infinite-dimensional Wiener process. It is well-known that the random attractor i…