Jaime San Martín

Description of the sub-Markov kernel associated to generalized ultrametric matrices. An algorithmic approach

Abstract We supply a simple algorithm which describes the sub-Markov kernel P associated to a nonsingular generalized ultrametric matrix U. This algorithm is based on the dyadic tree structure of U, it identifies the exiting roots of P and P t , and the couples i≠j for which P ij >0 (equivalently (U −1 ) ij ).

General change of variable formulas for semimartingales in one and finite dimensions

SummaryA general one dimensional change of variables formula is established for continuous semimartingales which extends the famous Meyer-Tanaka formula. The inspiration comes from an application arising in stochastic finance theory. For functions mapping ℝn to ℝ, a general change of variables formula is established for arbitrary semimartingales, where the usualC2 hypothesis is relaxed.

Linear Stochastic Differential Equations Driven by a Fractional Brownian Motion with Hurst Parameter Less than 1/2

Abstract In this article, we use the chaos decomposition approach to establish the existence of a unique continuous solution to linear fractional differential equations of the Skorohod type. Here, the coefficients are deterministic, the initial condition is anticipating and the underlying fractional Brownian motion has Hurst parameter less than 1/2. We provide an explicit expression for the chaos decomposition of the solution in order to show our results.

Rates of Decay and h-Processes for One Dimensional Diffusions Conditioned on Non-Absorption

AbstractLet (Xt) be a one dimensional diffusion corresponding to the operator

M

\mathcal{L} = \tfrac{1}{2}\partial _{xx} - \alpha \partial _x

Ratio limit theorem for parabolic horn-shaped domains

, starting from x>0 and T0 be the hitting time of 0. Consider the family of positive solutions of the equation

Optimal Selection of Customers for a Last-Minute Offer

{\mathcal{L}}\psi = - \lambda \psi