## Search

Now showing items 31-40 of 44

#### 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.

#### Cutting Brownian Paths

(American Mathematical Society, 1999-01)

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 ...

#### Minimal Fine Derivatives and Brownian Excursions

(Nagoya University, 1990-09)

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 ...

#### A critical case for Brownian slow points

(Springer-Verlag GmbH, 1996-01)

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 ...

#### Ito formula for an asymptotically 4-stable process

(Institute of Mathematical Statistics, 1996-02)

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

#### Eigenvalue expansions for Brownian motion with an application to occupation times

(Institute of Mathematical Statistics, 1996-01-31)

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 motion in a closed cone with vertex 0 until time one. We show that lim [subscript] u [approaching] 0 log P ...

#### Conditioned Brownian motion in planar domains

(Springer-Verlag GmbH, 1995-04)

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.

#### On domain monotonicity of the Neumann heat kernel

(Academic Press (Elsevier), 1993-08-15)

Some examples are given of convex domains for which domain monotonicity of the Neumann heat kernel does not hold.

#### Labyrinth dimension of Brownian trace

(Institute of Mathematics, 1995)

Suppose that X is a two-dimensional Brownian motion. The trace X[0, 1] contains a self-avoiding continuous path whose Hausdorff dimension is equal to 2.

#### Some path properties of iterated Brownian motion

(Birkhauser Boston, Inc., 1993)

The present paper is devoted to studying path properties of iterated Brownian motion (IBM). We want to examine how the lack of independence of increments influences the results and estimates which are well understood in the Brownian case. This may be viewed as a prelude to a deeper study of the process.