1. CMB 2013 (vol 57 pp. 585)
 Lehec, Joseph

Short Probabilistic Proof of the BrascampLieb and Barthe Theorems
We give a short proof of the BrascampLieb theorem, which asserts that
a certain general form of Young's convolution inequality is saturated
by Gaussian functions. The argument is inspired by Borell's stochastic
proof of the PrÃ©kopaLeindler inequality and applies also to the
reversed BrascampLieb inequality, due to Barthe.
Keywords:functional inequalities, Brownian motion Categories:39B62, 60J65 

2. CMB 2010 (vol 53 pp. 503)
 Kurenok, V. P.

The Time Change Method and SDEs with Nonnegative Drift
Using the time change method we show how to construct a solution to the stochastic equation $dX_t=b(X_{t})dZ_t+a(X_t)dt$ with a nonnegative drift $a$ provided there exists a solution to the auxililary equation $dL_t=[a^{1/\alpha}b](L_{t})d\bar Z_t+dt$ where $Z, \bar Z$ are two symmetric stable processes of the same index $\alpha\in(0,2]$. This approach allows us to prove the existence of solutions for both stochastic equations for the values $0<\alpha<1$ and only measurable coefficients $a$ and $b$ satisfying some conditions of boundedness. The existence proof for the auxililary equation uses the method of integral estimates in the sense of Krylov.
Keywords:Onedimensional SDEs, symmetric stable processes, nonnegative drift, time change, integral estimates, weak convergence Categories:60H10, 60J60, 60J65, 60G44 

3. CMB 2008 (vol 51 pp. 146)
 Zhou, Xiaowen

SteppingStone Model with Circular Brownian Migration
In this paper we consider the steppingstone model on a circle with
circular Brownian migration. We first point out a connection between
Arratia flow on the circle and the marginal distribution of this
model. We then give a new representation for the steppingstone
model using Arratia flow and circular coalescing Brownian motion.
Such a representation enables us to carry out some explicit
computations. In particular, we find the distribution for the first
time when there is only one type
left across the circle.
Keywords:steppingstone model, circular coalescing Brownian motion, Arratia flow, duality, entrance law Categories:60G57, 60J65 

4. CMB 1997 (vol 40 pp. 19)
 Derbez, Eric; Slade, Gordon

Lattice trees and superBrownian motion
This article discusses our recent proof that above eight dimensions
the scaling limit of sufficiently spreadout lattice trees is the variant
of superBrownian motion called {\it integrated superBrownian excursion\/}
($\ISE$), as conjectured by Aldous. The same is true for nearestneighbour
lattice trees in sufficiently high dimensions. The proof, whose details will
appear elsewhere, uses the lace expansion. Here, a related but simpler
analysis is applied to show that the scaling limit of a meanfield theory
is $\ISE$, in all dimensions. A connection is drawn between $\ISE$ and
certain generating functions and critical exponents, which may be useful
for the study of highdimensional percolation models at the critical point.
Categories:82B41, 60K35, 60J65 

5. CMB 1997 (vol 40 pp. 67)
 Knight, Frank B.

On a Brownian motion problem of T. Salisbury
Let $B$ be a Brownian motion on $R$, $B(0)=0$, and let
$f(t,x)$ be continuous. T.~Salisbury conjectured that if the total variation
of $f(t,B(t))$, $0\leq t\leq 1$, is finite $P$a.s., then $f$ does not
depend on $x$. Here we prove that this is true if the expected total
variation is finite.
Category:60J65 
