Wavelet Analysis and Covariance Structure of some Classes of Non-Stationary Processes.
Wavelet analysis of the multivariate fractional brownian motion
The work developed in the paper concerns the multivariate fractional Brownian motion (mfBm) viewed through the lens of the wavelet transform. After recalling some basic properties on the mfBm, we calculate the correlation structure of its wavelet transform. We particularly study the asymptotic behaviour of the correlation, showing that if the analyzing wavelet has a sufficient number of null first order moments, the decomposition eliminates any possible long-range (inter)dependence. The cross-spectral...
Wavelet coefficients of a gaussian process and applications
Wavelet construction of Generalized Multifractional processes.
Wavelet constructions in non-linear dynamics.
Wavelet estimation of the long memory parameter for Hermite polynomial of gaussian processes
We consider stationary processes with long memory which are non-Gaussian and represented as Hermite polynomials of a Gaussian process. We focus on the corresponding wavelet coefficients and study the asymptotic behavior of the sum of their squares since this sum is often used for estimating the long–memory parameter. We show that the limit is not Gaussian but can be expressed using the non-Gaussian Rosenblatt process defined as a Wiener–Itô integral of order 2. This happens even if the original...
Wavelet method for option pricing under the two-asset Merton jump-diffusion model
This paper examines the pricing of two-asset European options under the Merton model represented by a nonstationary integro-differential equation with two state variables. For its numerical solution, the wavelet-Galerkin method combined with the Crank-Nicolson scheme is used. A drawback of most classical methods is the full structure of discretization matrices. In comparison, the wavelet method enables the approximation of discretization matrices with sparse matrices. Sparsity is essential for the...
Wavelets, Generalized White Noise and Fractional Integration: The Synthesis of Fractional Brownian Motion.
Weak compactness and convergence in two-parameter martingale Hardy spaces and the dual of the VMO space.
Weak compactness in the space of martingales
Weak convergence of a Dirichlet-multinomial process.
Weak convergence of summation processes in Besov spaces
We prove invariance principles for partial sum processes in Besov spaces. This functional framework allows us to give a unified treatment of the step process and the smoothed process in the same parametric scale of function spaces. Our functional central limit theorems in Besov spaces hold for i.i.d. sequences and also for a large class of weakly dependent sequences.
Weak convergence to Ocone martingales: a remark.
Weak inequalities for exit times and analytic functions
Weak infinitesimal operators and stochastic differential games.
This article considers the problem of finding the optimal strategies in stochastic differential games with two players, using the weak infinitesimal operator of process xi the solution of d(xi) = f(xi,t,u1,u2)dt + sigma(xi,t,u1,u2)dW. For two-person zero-sum stochastic games we formulate the minimax solution; analogously, we perform the solution for coordination and non-cooperative stochastic differential games.
Weak quenched limiting distributions for transient one-dimensional random walk in a random environment
We consider a one-dimensional, transient random walk in a random i.i.d. environment. The asymptotic behaviour of such random walk depends to a large extent on a crucial parameter that determines the fluctuations of the process. When , the averaged distributions of the hitting times of the random walk converge to a -stable distribution. However, it was shown recently that in this case there does not exist a quenched limiting distribution of the hitting times. That is, it is not true that for...
Weak solutions for a simple hyperbolic system.
Weak solutions of stochastic differential inclusions and their compactness
In this paper, we consider weak solutions to stochastic inclusions driven by a semimartingale and a martingale problem formulated for such inclusions. Using this we analyze compactness of the set of solutions. The paper extends some earlier results known for stochastic differential inclusions driven by a diffusion process.
Weak solutions to stochastic differential equations driven by fractional Brownian motion
Existence of a weak solution to the -dimensional system of stochastic differential equations driven by a fractional Brownian motion with the Hurst parameter is shown for a time-dependent but state-independent diffusion and a drift that may by split into a regular part and a singular one which, however, satisfies the hypotheses of the Girsanov Theorem. In particular, a stochastic nonlinear oscillator driven by a fractional noise is considered.
Weak star convergence of martingales in a dual space
In this paper we present various weak star Kuratowski convergence results for multivalued martingales, supermartingales and multivalued mils in the dual of a separable Banach space. We establish several integral representation formulas for convex weak star compact valued multifunctions defined on a Köthe space and derive several existence results of conditional expectation for multivalued Gelfand-integrable multifunctions. Similar convergence results for Gelfand-integrable martingales in the dual...