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Quantitative Propagation of Chaos for Generalized Kacparticle Systems
(Inst Mathematical Statistics, 2016)
We study a class of one-dimensional particle systems with true (Bird type) binary interactions, which includes Kac's model of the Boltzmann equation and nonlinear equations for the evolution of wealth distribution arising ...
Fairy circles and their non-local stochastic instability
(Springer, 2017-02)
We study analytically a non local stochastic partial differential equation describing a fundamental mechanism for patterns formation, as the one responsible for the so called fairy circles appearing in two different ...
First-passage times for pattern formation in nonlocal partial differential equations
(American Physical Society, 2015-10)
We describe the lifetimes associated with the stochastic evolution from an unstable uniform state to a patterned one when the time evolution of the field is controlled by a nonlocal Fisher equation. A small noise is added ...
NOISE and ULTRAVIOLET DIVERGENCES IN SIMULATIONS of GINZBURG-LANDAU-LANGEVIN TYPE of EQUATIONS
(World Scientific Publ Co Pte Ltd, 2012-08-01)
The time evolution of an order parameter towards equilibrium can be described by nonlinear Ginzburg-Landau (GL) type of equations, also known as time-dependent nonlinear Schrodinger equations. Environmental effects of ...
Stochastic Integration With Respect to Cylindrical Semimartingales
(2021)
In this work we introduce a theory of stochastic integration with respect to general cylindrical semimartingales defined on a locally convex space Φ. Our construction of the stochastic integral is based on the theory of ...
Stochastic Path Perturbation Approach Applied to Non-Local Non-Linear Equations in Population Dynamics
(EDP Sciences, 2015-07)
We described the first passage time distribution associated to the stochastic evolution from an unstable uniform state to a patterned one (attractor of the system), when the time evolution is given by an integro-differential ...
Random fluctuations in nuclear reactors : stochastic point kinetics equations with two-energy groups
(Medellín - Colombia, 2022)
d-Dimensional KPZ equation as a stochastic gradient flow in an evolving landscape: Interpretation and time evolution of its generating functional
(Frontiers Media S.A., 2017-01-18)
The deterministic KPZ equation has been recently formulated as a gradient flow. Its non-equilibrium analog of a free energy-the "non-equilibrium potential" F[h], providing at each time the landscape where the stochastic ...
NOISE and ULTRAVIOLET DIVERGENCES IN SIMULATIONS of GINZBURG-LANDAU-LANGEVIN TYPE of EQUATIONS
(World Scientific Publ Co Pte Ltd, 2013)
The Stochastic Transport Dynamics of a Conserved Quantity on a Complex Network
(Nature Publishing Group, 2018)
© 2018, The Author(s). The stochastic dynamics of conserved quantities is an emergent phenomena observed in many complex systems, ranging from social and to biological networks. Using an extension of the Ehrenfest urn model ...