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Now showing items 1-10 of 32

#### Intersection local time for points of infinite multiplicity

(Institute of Mathematical Statistics, 1994-04)

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 two-dimensional Brownian motion spends a units of local time. The measure [beta] [subscript] a is carried by a set which has Hausdorff dimension equal to 2−a. A Palm measure ...

#### Variably skewed Brownian motion

(Institute of Mathematical Statistics, 2000-03-01)

Given a standard Brownian motion B, we show that the equation X [subscript] t = x [subscript] 0 + B [subscript] t + [beta](L [to the power of X] [subscript] t ); t [is greater than or equal to] 0 ; has a unique strong solution X. Here L [to the power of X] is the symmetric local time of X at 0, and [beta] is a given differentiable ...

#### On minimal parabolic functions and time-homogenous parabolic h-transforms

(American Mathematical Society, 1999-03-29)

Does a minimal harmonic function h remain minimal when it is viewed as a parabolic function? The question is answered for a class of long thin
semi-infinite tubes D [is an element of the subset of real numbers to the power of] d of variable width and minimal harmonic functions h corresponding to the boundary point of D "at ...

#### 2-D Brownian motion in a system of traps: Application of conformal transformations

(Institute of Physics, 1992)

We study two-dimensional Brownian motion in a periodic system of traps using conformal transformations. The system is periodic in the x and y directions. We calculate the ratio of the drift along the y-axis to the drift along the x-axis. The drift of the Brownian particle is induced by conditioning and by the asymmetry of
the ...

#### A representation of local time for Lipschitz surfaces

(Springer-Verlag GmbH, 1990)

Suppose that D [is an element of the set of Real numbers to the power of n], n [is greater than or equal to] 2, is a Lipschitz domain and let N[subscript]t(r) be the number of excursions of Brownian motion inside D with diameter greater than r which started before time t. Then rN[subscript]t(r) converges as r --> 0 to a ...

#### Cut points on Brownian paths

(Institute of Mathematical Statistics, 1989-07)

Let X be a standard two-dimensional Brownian motion. There exists a.s. t [is an element of the set] (0; 1) such that X([0; t))[intersected with] X((t; 1]) = [empty set]. It follows that X([0; 1]) is not
homeomorphic to the Sierpinski carpet a.s.

#### 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.

#### Non-polar points for reflected Brownian motion

(Elsevier, 1993)

Our main results are (i) a new construction of reflected Brownian motion X in a half-plane with non-smooth angle of oblique reflection and
(ii) a theorem on existence of some "exceptional" points on the paths of the standard two-dimensional Brownian motion. The link between these two seemingly disparate results will be formed ...

#### Stochastic bifurcation models

(Institute of Mathematical Statistics, 1999-01)

We study an ordinary differential equation controlled by a stochastic process. We present results on existence and uniqueness of solutions, on associated local times (Trotter and Ray-Knight theorems), and on time and direction of bifurcation. A relationship with Lipschitz approximations to Brownian paths is also discussed.

#### An asymptotically 4-stable process

(CRC Press, 1995)

An asymptotically 4-stable process is constructed. The model identifies the 4-stable process with a sequence of processes converging in a very weak sense. It is proved that the 4-th variation of the process is a linear function of time and its quadratic variation may be identified with a Brownian motion.