Browsing EPrint Collection  Mathematics by Issue Date
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The Martin boundary in nonLipschitz domains
(American Mathematical Society, 1993)The Martin boundary with respect to the Laplacian and with respect to uniformly elliptic operators in divergence form can be identified with the Euclidean boundary in C [to the power of gamma] domains, where [gamma](x) = ... 
Excursion laws and exceptional points on Brownian paths
(SpringerVerlag, 1993)The purpose of this note is to present an example of a family of "exceptional points" on Brownian paths which cannot be constructed using an entrance law. 
Nonpolar points for reflected Brownian motion
(Elsevier, 1993)Our main results are (i) a new construction of reflected Brownian motion X in a halfplane with nonsmooth angle of oblique reflection and (ii) a theorem on existence of some "exceptional" points on the paths of the ... 
On domain monotonicity of the Neumann heat kernel
(Academic Press (Elsevier), 19930815)Some examples are given of convex domains for which domain monotonicity of the Neumann heat kernel does not hold. 
The boundary Harnack principle for nondivergence form elliptic operators
(Cambridge University Press, 1994)If L is a uniformly elliptic operator in non–divergence form, the boundary Harnack principle for the ratio of positive L–harmonic functions holds in Hölder domains of order [alpha] if [alpha] > 1/2. A counterexample shows ... 
Variation of iterated Brownian motion
(American Mathematical Society, 1994)In this paper, we study higher order variations of iterated Brownian motion (IBM) with view towards possible applications to the construction of the stochastic integral with respect to IBM. We prove that the 4th variation ... 
2D Brownian motion in a system of reflecting barriers: effective diffusivity by a sampling method
(Institute of Physics, 19940207)We study twodimensional Brownian motion in an ordered periodic system of linear reflecting barriers using the sampling method and conformal transformations. We calculate the effective diffusivity for the Brownian particle. ... 
Intersection local time for points of infinite multiplicity
(Institute of Mathematical Statistics, 199404)For each a [is an element of the set] (0, 1/2), there exists a random measure [beta] [subscript] a which is supported on the set of points where twodimensional Brownian motion spends a units of local time. The measure ... 
The level sets of iterated Brownian motion
(SpringerVerlag, 1995)We show that the Hausdorff dimension of every level set of iterated Brownian motion is equal to 3/4. 
Labyrinth dimension of Brownian trace
(Institute of Mathematics, 1995)Suppose that X is a twodimensional Brownian motion. The trace X[0, 1] contains a selfavoiding continuous path whose Hausdorff dimension is equal to 2. 
An asymptotically 4stable process
(CRC Press, 1995)An asymptotically 4stable process is constructed. The model identifies the 4stable process with a sequence of processes converging in a very weak sense. It is proved that the 4th variation of the process is a linear ... 
A Skorobodtype lemma and a decomposition of reflected Brownian motion
(Institute of Mathematical Statistics, 199504)We consider twodimensional reflected Brownian motions in sharp thorns pointed downward with horizontal vectors of reflection. We present a decomposition of the process into a Brownian motion and a process which has bounded ... 
Conditioned Brownian motion in planar domains
(SpringerVerlag GmbH, 199504)We give an upper bound for the Green functions of conditioned Brownian motion in planar domains. A corollary is the conditional gauge theorem in bounded planar domains. 
Iterated law of iterated logarithm
(Institute of Mathematical Statistics, 199510)Suppose [epsilon] [is a member of the set] [0, 1) and let theta [subscipt epsilon] (t) = (1 − [epsilon]) [square root of] (2tln [subscript] 2 t). Let L [to the power of epsilon] [subscript] t denote the amount of local ... 
A critical case for Brownian slow points
(SpringerVerlag GmbH, 199601)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 ... 
No triple point of planar Brownian motion is accessible
(Institute of Mathematical Statistics, 199601)We show that the boundary of a connected component of the complement of a planar Brownian path on a fixed timeinterval contains almost surely no triple point of this Brownian path. 
Eigenvalue expansions for Brownian motion with an application to occupation times
(Institute of Mathematical Statistics, 19960131)Let B be a Borel subset of R [to the power of] d with finite volume. We give an eigenvalue expansion for the transition densities of Brownian motion killed on exiting B. Let A [subscript] 1 be the time spent by Brownian ... 
Ito formula for an asymptotically 4stable process
(Institute of Mathematical Statistics, 199602)An Itotype formula is given for an asymptotically 4stable process. 
Configurational transition in a FlemingViottype model and probabilistic interpretation of Laplacian eigenfunctions
(Institute of Physics, 19960607)We analyze and simulate a twodimensional Brownian multitype particle system with death and branching (birth) depending on the position of particles of different types. The system is confined in the twodimensional box, ...