A popular theory of business cycles is that they are driven by animal spirits: shifts in expectations brought on by sunspots. A prominent example is Howitt and McAfee (AER, 1992). We show that this model has a unique equilibrium if there are payoff shocks of any size. This equilibrium still has the desirable property that ...

A pair (X; Y) of Markov processes is called a Markov coupling if X and Y have the same transition probabilities and (X;Y) is a Markov process. We say that a coupling is "shy" if there exists a (random) [Epsilon] > 0 such that dist(X [subscript] t; Y [subscript] t) > [Epsilon] for all t [is greater than or equal to] 0. We ...

Consider an open set D [is an element of the set] R [The set of Real Numbers] [superscript]d, d [is greater than or equal to] 2, and a closed ball B [is a proper subset of] D. Let E[superscript]xT[subscript]B denote the expectation of the hitting time of B for reflected Brownian motion in D starting from x [is an element of ...

There exists a planar domain with piecewise smooth boundary and one hole such that the second eigenfunction for the Laplacian with Neumann boundary conditions attains its maximum and minimum inside the domain.

We consider two species of particles performing random walks in a domain in [Real numbers] [superscript] d with reflecting boundary conditions, which annihilate on contact. In addition there is a conservation law so that the total number of particles of each type is preserved: When the two particles of different species ...

We discuss the relationships between the notion of intrinsic ultracontractivity, parabolic Harnack principle, compactness of the 1-resolvent of the Neumann Laplacian, and non-trap property for Euclidean domains with finite Lebesgue measure. In particular, we give an answer to an open problem raised by Davies and Simon in 1984 ...

For every bounded planar domain D with a smooth boundary, we define a "Lyapunov exponent" [Lambda](D) using a fairly explicit formula. We consider two reflected Brownian motions in D, driven by the same Brownian motion (i.e., a "synchronous coupling"). If [Lambda] (D) > 0 then the distance between the two Brownian particles ...

A popular theory of business cycles is that they are driven by animal spirits: shifts in expectations brought on by sunspots. A prominent example is Howitt and McAfee (AER, 1992). We show that this model has a unique equilibrium if there are payoff shocks of any size. This equilibrium still has the desirable property that ...

A lip domain is a Lipschitz domain where the Lipschitz constant is strictly less than one. We prove strong existence and pathwise uniqueness for the solution X = {X [subscript] t, t [is less than or equal to] 0} to the Skorokhod equation dX [subscript] t = dW [subscript] t + n(X [subscript] t)dL [subscript] t, in planar lip ...

We prove that the sequence of finite reflecting branching Brownian motion forests defined by Burdzy and Le Gall ([?]) converges in probability to the "super-Brownian motion with reflecting historical paths." This solves an open problem posed in [?], where only tightness was proved for the sequence of approximations. Several ...