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#### 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 ...

#### 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.

#### Coalescence of skew Brownian motions

(Springer-Verlag, 2001)

The purpose of this short note is to prove almost sure coalescence of two skew Brownian motions starting from different initial points, assuming that they are driven by the same Brownian motion. The result is very simple but we would like to record it in print as it has already become the foundation of a research project of ...