We consider a stochastic flow in which individual particles follow skew Brownian motions, with each one of these processes driven by the same Brownian motion. One does not have uniqueness for the solutions of the corresponding stochastic differential equation simultaneously for all real initial conditions. Due to this lack ...

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 ...

The paper studies, among other things, two types of possible singularities of the solution to the heat equation at the boundary of a moving domain. Several explicit results on "heat atoms" and "heat singularities" are given.

We present a stochastic process with sawtooth paths whose distribution is given by a simple rule and whose stationary distribution is Gaussian. The process arose in a natural way in research on interaction of an inert particle with a Brownian particle.

The system for publishing mathematical articles should be reformed and the new system should resemble, on the economic side, the bottled water industry. My main theses are: (i) the results of the mathematical research should be available to the public just like tap water, (ii) the role of the commercial (and non-commercial) ...

Let Z [subscript] t be two-dimensional Brownian motion. We say that a straight line L is a cut line if there exists a time t [is an element of the set] (0, 1) such that the trace of {Z [subscript] s : 0 [is less than or equal to] s < t} lies on one side of L and the trace of {Z [subscript] s : t < s < 1} lies on the other ...

In this paper, we continue the study initiated in Burdzy and Williams (1986) of the local properties of Brownian excursions in Lipschitz domains. The focus in part I was on local path properties of such excursions. In particular, a necessary and sufficient condition was given for Brownian excursions in a Lipschitz domain to ...

Let f be an analytic function defined on D [is a subset of] [complex numbers] C. If [the derivative of the function f at the point x] has a limit when [the set] x [into the set] z [is an element of the set partial derivative] D in the minimal fine topology then the limit will be called a minimal fine derivative. Several ...

Let X [subscript] t be a Brownian motion and let S(c) be the set of reals r [is greather than or equal to] 0 such that |X ([subscript] r+t) − X [subscript] r| [is less than or equal to] c [square root of] t, 0 [is less than or equal to] t [is less than or equal to] h, for some h = h(r) > 0. It is known that S(c) is empty if ...

An Ito-type formula is given for an asymptotically 4-stable process.