Soledad Torres

Donsker type theorem for the Rosenblatt process and a binary market model

Abstract In this article, we prove a Donsker type approximation theorem for the Rosenblatt process, which is a selfsimilar stochastic process exhibiting long range dependence. We use this result to construct a binary market model driven by this process and we show that the model admits arbitrage opportunities. Finally we present some numerical simulations to illustrate the method of approximation.

Maximum likelihood estimators and random walks in long memory models

We consider statistical models driven by Gaussian and non-Gaussian self-similar processes with long memory and we construct maximum-likelihood estimators for the drift parameter. Our approach is based on the non-Gaussian case on the approximation by random walks of the driving noise. We study the asymptotic behaviour of the estimators and we give some numerical simulations to illustrate our results.

Full Bayesian Analysis for a Class of Jump-Diffusion Models

The Full Bayesian Significance Test (FBST) is adjusted for jump detection in a diffusion process. Under a natural parameterization, pure diffusion can be seen as a precise hypothesis. The evidence measure defined by FBST deals with absolutely continuous posterior distributions, when posterior rates for precise hypotheses are not appropriate. Applications to simulated and real data are shown.

Comparative Estimation for Discrete Fractional Ornstein-Uhlenbeck Process

We compare, theoretically and numerically, the maximum likelihood and the Bayes estimators for discretely observed fractional diffusions.

The Molecular Chaperone Hsc70 Interacts with Tyrosine Hydroxylase to Regulate Enzyme Activity and Synaptic Vesicle Localization.

We previously reported that the vesicular monoamine transporter 2 (VMAT2) is physically and functionally coupled with Hsc70 as well as with the dopamine synthesis enzymes tyrosine hydroxylase (TH) and aromatic amino acid decarboxylase, providing a novel mechanism for dopamine homeostasis regulation. Here we expand those findings to demonstrate that Hsc70 physically and functionally interacts with TH to regulate the enzyme activity and synaptic vesicle targeting. Co-immunoprecipitation assays performed in brain tissue and heterologous cells demonstrated that Hsc70 interacts with TH and aromatic amino acid decarboxylase. Furthermore, in vitro binding assays showed that TH directly binds the substrate binding and carboxyl-terminal domains of Hsc70. Immunocytochemical studies indicated that Hsc70 and TH co-localize in midbrain dopaminergic neurons. The functional significance of the Hsc70-TH interaction was then investigated using TH activity assays. In both dopaminergic MN9D cells and mouse brain synaptic vesicles, purified Hsc70 facilitated an increase in TH activity. Neither the closely related protein Hsp70 nor the unrelated Hsp60 altered TH activity, confirming the specificity of the Hsc70 effect. Overexpression of Hsc70 in dopaminergic MN9D cells consistently resulted in increased TH activity whereas knockdown of Hsc70 by short hairpin RNA resulted in decreased TH activity and dopamine levels. Finally, in cells with reduced levels of Hsc70, the amount of TH associated with synaptic vesicles was decreased. This effect was rescued by addition of purified Hsc70. Together, these data demonstrate a novel interaction between Hsc70 and TH that regulates the activity and localization of the enzyme to synaptic vesicles, suggesting an important role for Hsc70 in dopamine homeostasis.

Euler scheme for solutions of a countable system of stochastic differential equations

We consider a countable system of stochastic differential equation. Euler scheme for approximating these solutions is used, and the global error is estimated. Solutions are approximated by means of a process which takes values in a finite dimensional space. Finally, we expand the global error for a class of smooth functions in powers of the discretization step size.

The Euler scheme for Hilbert space valued stochastic differential equations

Here we consider stochastic differential equations whose solutions take values in a Hilbert space. The Euler Scheme for approximating these solutions is used, and the global error is estimated. In addition, solutions are approximated by means of a process which takes values in a finite-dimensional subspace.

A Simulation-Based Study on Bayesian Estimators for the Skew Brownian Motion

In analyzing a temporal data set from a continuous variable, diffusion processes can be suitable under certain conditions, depending on the distribution of increments. We are interested in processes where a semi-permeable barrier splits the state space, producing a skewed diffusion that can have different rates on each side. In this work, the asymptotic behavior of some Bayesian inferences for this class of processes is discussed and validated through simulations. As an application, we model the location of South American sea lions (Otaria flavescens) on the coast of Calbuco, southern Chile, which can be used to understand how the foraging behavior of apex predators varies temporally and spatially.

Class of skew-distributions: theory and applications in biology

In this paper, we study a class of skew-normal distributions driven by the convolution of two independent random variables: a normal and a beta distributed random variables. This problem is motivated by the numerical simulation of the oviductal egg transport in mammals, expressed as a series of microsphere instant velocities regulated by ovarian hormones including estradiol. We propose a closed form convolution formula, represented in terms of the infinite series expanded using Hermite polynomials. We also analyse the convergence of such series and perform the numerical experiments to illustrate these formulae.

The Euler scheme for a class of anticipating stochastic differential equations

Using the techniques of the Malliavin calculus and standard Itô calculus methods, we give an Euler scheme to approximate the solution of a class of anticipating stochastic differential equations.