Related papers: On Equilibrium Determinacy in Overlapping Generati…

A combination of implicit and explicit timestepping is analyzed for a system of ODEs motivated by ones arising from spatial discretizations of evolutionary partial differential equations. Loosely speaking, the method we consider is implicit…

We pursue robust approach to pricing and hedging in mathematical finance. We consider a continuous time setting in which some underlying assets and options, with continuous paths, are available for dynamic trading and a further set of…

Financial markets are prominent examples for highly non-stationary systems. Sample averaged observables such as variances and correlation coefficients strongly depend on the time window in which they are evaluated. This implies severe…

Since the advent of inflation, several theorems have been proven suggesting that although inflation can (and generically does) continue eternally into the future, it cannot be extended eternally into the past to create a ``steady-state''…

The optimal (`equilibrium') macroscopic properties of an economy with $N$ industries endowed with different technologies, $P$ commodities and one consumer are derived in the limit $N\to\infty$ with $n=N/P$ fixed using the replica method.…

We analyze the long-term stability of a stochastic model designed to illustrate the adaptation of a population to variation in its environment. A piecewise-deterministic process modeling adaptation is coupled to a Feller logistic diffusion…

A new definition of continuous-time equilibrium controls is introduced. As opposed to the standard definition, which involves a derivative-type operation, the new definition parallels how a discrete-time equilibrium is defined, and allows…

Using the Fermi Golden Rule analysis developed in several results by the first author, we prove asymptotic stability of asymmetric nonlinear bound states bifurcating from linear bound states for a quintic nonlinear Schr\"odinger operator…

Periodically forced turbulence is used as a test case to evaluate the predictions of two-equation and multiple-scale turbulence models in unsteady flows. The limitations of the two-equation model are shown to originate in the basic…

Discrete-time models of non-uniformly sampled nonlinear systems under zero-order hold relate the next state sample to the current state sample, (constant) input value, and sampling interval. The exact discrete-time model, that is, the…

We consider the 1D linear Schr{\"o}dinger equation, on a bounded interval, with Dirichlet boundary conditions and bilinear scalar control. The small-time local exact controllability around the ground state was proved in [BeaLau10], under an…

This paper studies the well-posedness of a class of nonlocal parabolic partial differential equations (PDEs), or equivalently equilibrium Hamilton-Jacobi-Bellman equations, which has a strong tie with the characterization of the equilibrium…

We consider a system of nonlinear partial differential equations that describes an age-structured population inhabiting several temporally varying patches. We prove existence and uniqueness of solution and analyze its large-time behavior in…

Existence of nontrivial nonnegative equilibrium solutions for age structured population models with nonlinear diffusion is investigated. Introducing a parameter measuring the intensity of the fertility, global bifurcation is shown of a…

In this paper, we use a variety of mathematical techniques to explore existence, local stability, and global stability of equilibria in abstract models of mitochondrial metabolism. The class of models constructed is defined by the…

This paper proves the existence and uniqueness results (in the sense of maximally defined regularity) as well as the stability analysis for the solutions to a class of nonlocal fully-nonlinear parabolic systems, where the nonlocality stems…

Transition rates in continuously driven steady states were derived in [Evans R M L, 2005 J. Phys. A: Math. Gen. 38, 293] by demanding that no information other than the microscopic laws of motion and the macroscopic observables of the…

We introduce a notion of local Hilbert--Schmidt stability, motivated by the recent definition by Bradford of local permutation stability, and give examples of (non-residually finite) groups that are locally Hilbert--Schmidt stable but not…

We consider the pricing of derivatives in a setting with trading restrictions, but without any probabilistic assumptions on the underlying model, in discrete and continuous time. In particular, we assume that European put or call options…

Rational pure bubble models feature multiple (and often a continuum of) equilibria, which makes model predictions and policy analyses non-robust. We show that when the interest rate in the fundamental equilibrium is below the economic…