Analysis of nonlinear noisy integrate & fire neuron models: blow-up and steady states
MJ Cáceres, JA Carrillo, B Perthame - The Journal of Mathematical …, 2011 - Springer
Abstract Nonlinear Noisy Leaky Integrate and Fire (NNLIF) models for neurons networks can
be written as Fokker-Planck-Kolmogorov equations on the probability density of neurons, the …
be written as Fokker-Planck-Kolmogorov equations on the probability density of neurons, the …
Classical solutions for a nonlinear Fokker-Planck equation arising in computational neuroscience
In this paper we analyze the global existence of classical solutions to the initial boundary-
value problem for a nonlinear parabolic equation describing the collective behavior of an …
value problem for a nonlinear parabolic equation describing the collective behavior of an …
Global existence and uniqueness of solutions to a model of price formation
L Chayes, M del Mar González, MP Gualdani… - SIAM Journal on …, 2009 - SIAM
Global Existence and Uniqueness of Solutions to a Model of Price Formation Page 1 Copyright
© by SIAM. Unauthorized reproduction of this article is prohibited. SIAM J. MATH. ANAL. c …
© by SIAM. Unauthorized reproduction of this article is prohibited. SIAM J. MATH. ANAL. c …
High-frequency simulations of an order book: a two-scale approach
CA Lehalle, O Guéant, J Razafinimanana - Econophysics of Order-driven …, 2011 - Springer
Abstract Models of market microstructure at the order book scale can be split into two
families: First, the agent-based models [5] aiming at simulating a large number of agents …
families: First, the agent-based models [5] aiming at simulating a large number of agents …
Asymptotics for a free boundary model in price formation
M del Mar González, MP Gualdani - Nonlinear Analysis: Theory, Methods & …, 2011 - Elsevier
We study the asymptotics for a large time of solutions to a one-dimensional parabolic
evolution equation with non-standard measure-valued right hand side, that involves …
evolution equation with non-standard measure-valued right hand side, that involves …
Parabolic free boundary price formation models under market size fluctuations
In this paper we propose an extension of the Lasry--Lions price formation model which
includes fluctuations of the numbers of buyers and vendors. We analyze the model in the …
includes fluctuations of the numbers of buyers and vendors. We analyze the model in the …
Instability and bifurcation in a trend depending price formation model
MM González Nogueras, MP Gualdani… - Acta applicandae …, 2016 - upcommons.upc.edu
A well-known model due to J.-M. Lasry and PL Lions that presents the evolution of prices in
a market as the evolution of a free boundary in a diffusion equation is modified in order to …
a market as the evolution of a free boundary in a diffusion equation is modified in order to …
Instability and bifurcation in a trend depending price formation model
MM González, MP Gualdani, J Solà-Morales - Acta Applicandae …, 2016 - Springer
A well-known model due to J.-M. Lasry and PL Lions that presents the evolution of prices in
a market as the evolution of a free boundary in a diffusion equation is modified in order to …
a market as the evolution of a free boundary in a diffusion equation is modified in order to …
Some non-standard Sobolev spaces, interpolation and its application to PDE
MM González, MP Gualdani - Acta applicandae mathematicae, 2012 - Springer
We consider some nonstandard Sobolev spaces in one dimension, in which functions have
different regularity in different subsets. These spaces are useful in the study of some …
different regularity in different subsets. These spaces are useful in the study of some …
[PDF][PDF] ANALYSIS OF CONVERGENCE TO EQUILIBRIUM FOR A
R Xu - 2009 - scholarworks.calstate.edu
CALIFORNIA STATE UNIVERSITY, NORTHRIDGE ANALYSIS OF CONVERGENCE TO
EQUILIBRIUM FOR A MODEL OF PRICE FORMATION A thesis submitted Page 1 CALIFORNIA …
EQUILIBRIUM FOR A MODEL OF PRICE FORMATION A thesis submitted Page 1 CALIFORNIA …