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Now showing items 41-50 of 84

#### Non-intersection exponents for Brownian paths. Part I: Existence and an invariance principle

(Springer-Verlag GmbH, 1990)

Let X and Y be independent three-dimensional Brownian motions, X(0) = (0; 0; 0), Y (0) = (1; 0; 0) and let p [subscript]r = P(X[0; r] [intersected with] Y [0; r] = [empty set]. Then the "non-
intersection exponent" [from] lim [subscript]r [to infinity] -log p [subscript]r / log r exists and is equal to a similar "non-intersection ...

#### Curvature of the convex hull of planar Brownian motion near its minimum point

(North-Holland (Elsevier), 1989-10)

Let f be a (random) real-valued function whose graph represents the boundary of the convex hull of planar Brownian motion run until time 1 near its lowest point in a coordinate system so that f is non-negative and f(0) = 0. The ratio of f(x) and |x|/|log |x|| oscillates near 0 between 0 and infinity a.s.

#### Stable processes have thorns

(Institute of Mathematical Statistics, 2003-01)

Let X(t) be the symmetric [alpha]-stable process in R [to the power of] d, [alpha is an element of the set] (0, 2), d [is greater than or equal to] 2. For f : (0, 1) [approaching] (0,[infinity]) let D(f) be the thorn {x [is an element of the set] R [to the power of] d : x [subscript]1 [is an element of the set] (0, 1), |(x ...

#### On nodal lines of Neumann eigenfunctions

(Institute of Mathematical Statistics, 2002-06-03)

We present a new method for locating the nodal line of the second eigenfunction for the Neumann problem in a planar domain.

#### Stochastic differential equations driven by stable processes for which pathwise uniqueness fails

(North-Holland (Elsevier), 2004-05)

Let Z [subscript] t be a one-dimensional symmetric stable process of order [alpha] with [alpha is an element of the set] (0, 2) and consider the stochastic differential equation
dX [subscript] t = [omega] (X [subscript] t−)dZ [subscript]t.
For [beta] < 1 [divided by alpha] ^ 1, we show there exists a function that is ...

#### On the time and direction of stochastic bifurcation

(Elsevier, 1998)

This paper is a mathematical companion to an article introducing a new economics model, by Burdzy, Frankel and Pauzner (1997). The motivation of this paper is applied, but the results may have some mathematical interest in their own right. Our model, i.e., equation (1.1) below, does not seem to be known in literature. Despite ...

#### Positivity of Brownian transition densities

(Electronic Journal of Probability, 1997-09-24)

Let B be a Borel subset of R [to the power of] d and let p(t, x, y) be the transition densities of Brownian motion killed on leaving B. Fix x and y in B. If p(t, x, y) is positive for one t, it is positive for every value of t. Some related results are given.

#### Lifetimes of conditioned diffusions

(Springer-Verlag GmbH, 1992)

We investigate when an upper bound on expected lifetimes of conditioned diffusions associated with elliptic operators in divergence and non-divergence form can be found. The critical value of the parameter is found for each of the following classes of domains: L [to the power of p] domains (p = n − 1), uniformly regular twisted ...

#### Coalescence of skew Brownian motions

(Springer-Verlag, 2001)

The purpose of this short note is to prove almost sure coalescence of two skew Brownian motions starting from different initial points, assuming that they are driven by the same Brownian motion. The result is very simple but we would like to record it in print as it has already become the foundation of a research project of ...

#### Shocks and business cycles

(Berkeley Electronic Press, 2005)

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 ...