A Characterization Of Cramér Representation Of Stochastic Processes
A characterization of Cramér representation of stochastic processes.
A differentiable isomorphism between Wiener space and path group
A discrete stochastic Korovkin theorem.
A mathematical framework for learning and adaption: (generalized) random systems with complete connections.
The aim of this paper is to show that the theory of (generalized) random systems with complete connection may serve as a mathematical framework for learning and adaption. Chapter 1 is of an introductory nature and gives a general description of the problems with which one is faced. In Chapter 2 the mathematical model and some results about it are explained. Chapter 3 deals with special learning and adaption models.
A remark on disjointness results for stable processes
A representation result for time-space brownian chaos
A system of functional-differential equations associated with the optimal detection problem for jump-times of a Poisson process.
Adaptive density estimation under weak dependence
Assume that (Xt)t∈Z is a real valued time series admitting a common marginal density f with respect to Lebesgue's measure. [Donoho et al. Ann. Stat.24 (1996) 508–539] propose near-minimax estimators based on thresholding wavelets to estimate f on a compact set in an independent and identically distributed setting. The aim of the present work is to extend these results to general weak dependent contexts. Weak dependence assumptions are expressed as decreasing bounds of covariance terms and are...
Adaptive wavelet estimation of the diffusion coefficient under additive error measurements
We study nonparametric estimation of the diffusion coefficient from discrete data, when the observations are blurred by additional noise. Such issues have been developed over the last 10 years in several application fields and in particular in high frequency financial data modelling, however mainly from a parametric and semiparametric point of view. This paper addresses the nonparametric estimation of the path of the (possibly stochastic) diffusion coefficient in a relatively general setting. By...
Algebraic polynomials with random coefficients.
Algebraic polynomials with random coefficients with binomial and geometric progressions.
Almost Sure Sampling Reconstruction Of Non-Band-Limited Homogeneous Random Fields
Analytic stochastic processes II
Application du calcul symbolique au calcul de la loi de certains processus
Application d'un théorème de G. Mokobodzki à la théorie des flots
Applications of time-delayed backward stochastic differential equations to pricing, hedging and portfolio management in insurance and finance
We investigate novel applications of a new class of equations which we call time-delayed backward stochastic differential equations. Time-delayed BSDEs may arise in insurance and finance in an attempt to find an investment strategy and an investment portfolio which should replicate a liability or meet a target depending on the strategy applied or the past values of the portfolio. In this setting, a managed investment portfolio serves simultaneously as the underlying security on which the liability/target...
Approximate Aggregation Methods in Discrete Time Stochastic Population Models
Approximate aggregation techniques consist of introducing certain approximations that allow one to reduce a complex system involving many coupled variables obtaining a simpler ʽʽaggregated systemʼʼ governed by a few variables. Moreover, they give results that allow one to extract information about the complex original system in terms of the behavior of the reduced one. Often, the feature that allows one to carry out such a reduction is the presence...
Arbitrage for simple strategies
Various aspects of arbitrage on finite horizon continuous time markets using simple strategies consisting of a finite number of transactions are studied. Special attention is devoted to transactions without shortselling, in which we are not allowed to borrow assets. The markets without or with proportional transaction costs are considered. Necessary and sufficient conditions for absence of arbitrage are shown.
Asymptotics for random walks with dependent heavy-tailed increments.