Bounded Laws of the Iterated Logarithm for Quadratic Forms in Gaussian Random Variables.
Bounds for disconnection exponents.
Bounds for the range of American contingent claim prices in the jump-diffusion model
The problem of valuation of American contingent claims for a jump-diffusion market model is considered. Financial assets are described by stochastic differential equations driven by Gaussian and Poisson random measures. In such setting the money market is incomplete, thus contingent claim prices are not uniquely defined. For different equivalent martingale measures different arbitrage free prices can be derived. The problem is to find exact bounds for the set of all possible prices obtained in this...
Branching brownian motion with an inhomogeneous breeding potential
This article concerns branching brownian motion (BBM) with dyadic branching at rate β|y|p for a particle with spatial position y∈ℝ, where β>0. It is known that for p>2 the number of particles blows up almost surely in finite time, while for p=2 the expected number of particles alive blows up in finite time, although the number of particles alive remains finite almost surely, for all time. We define the right-most particle, Rt, to be the supremum of the spatial positions of the particles...
Branching processes, the Ray-Knight theorem, and sticky brownian motion
Brownian bridge asymptotics for random -mappings.
Brownian couplings, convexity, and shyness.
Brownian excursion area, wright's constants in graph enumeration, and other Brownian areas.
Brownian excursion conditioned on its local time.
Brownian Excursions and Minimal Thinness. Part III: Applications to the Angular Derivative Problem.
Brownian excursions from extremes
Brownian excursions, stochastic integrals, and representation of Wiener functionals.
Brownian filtrations are not stable under equivalent time-changes
Brownian local minima, random dense countable sets and random equivalence classes.
Brownian local times.
Brownian local times and branching processes
Brownian Motion and Eigenvalues for the Dirichlet Laplacian.
Brownian motion and generalized analytic and inner functions
Let be a mapping from an open set in into , with . To say that preserves Brownian motion, up to a random change of clock, means that is harmonic and that its tangent linear mapping in proportional to a co-isometry. In the case , , such conditions signify that corresponds to an analytic function of one complex variable. We study, essentially that case , , in which we prove in particular that such a mapping cannot be “inner” if it is not trivial. A similar result for , would solve...
Brownian motion and parabolic Anderson model in a renormalized Poisson potential
A method known as renormalization is proposed for constructing some more physically realistic random potentials in a Poisson cloud. The Brownian motion in the renormalized random potential and related parabolic Anderson models are modeled. With the renormalization, for example, the models consistent to Newton’s law of universal attraction can be rigorously constructed.
Brownian motion and random walks on manifolds
We develop a procedure that allows us to “descretise” the Brownian motion on a Riemannian manifold. We construct thus a random walk that is a good approximation of the Brownian motion.