Teresa Martinez

On Stochastic Differential Equations with Locally Unbounded Drift

We study the regularizing effect of the noise on differential equations with irregular coefficients. We present existence and uniqueness theorems for stochastic differential equations with locally unbounded drift.

Riesz transforms related to Bessel operators

Riesz transforms

On numerical solution of stochastic partial differential equations of elliptic type

R_\mu

Boundedness of vector-valued martingale transforms on extreme points and applciations

related to the Bessel operators

BMO spaces related to Schrödinger operators with potentials satisfying a reverse Hölder inequality

\Delta_\mu=x^{-\mu-1/2}Dx^{2\mu+1}Dx^{-\mu-1/2}

Operator-valued martingale transforms

are studied in this work. We develop for

A Lattice Scheme for Stochastic Partial Differential Equations of Elliptic Type in Dimension d ź 4

R_\mu

Riesz transform and g-function associated with Bessel operators and their appropriate Banach spaces

a theory that runs parallel to that for the Euclidean Hilbert transform. It is proved that