Ayache, Antoine Esser, Céline Qidi, Peng

We focus on a stochastic process $\{Y(t)\}_{t\in [0,v]}$ defined by a pathwise Young integral of a general form. Thanks to the Haar basis, we connect the classical method of approximation of $\{Y(t)\}_{t\in [0,v]}$ through Euler scheme and Riemann-Stieltjes sums with a new approach consisting in the use of an appropriate series representation of $\...

Sun, Xu Duan, Jinqiao Li, Xiaofan
Published in
Nonlinear Dynamics

A stochastic differential equation model is considered for nonlinear oscillators under excitations of combined Gaussian and Poisson white noise. Since the solutions of stochastic differential equations can be interpreted in terms of several types of stochastic integrals, it is sometimes confusing about which integral is actually appropriate. In ord...

Hamdi, Tarek

My PhD work is composed of two parts, the first part is dedicated to the discrete-time stochastic analysis for obtuse random walks as to the second part, it is linked to free probability. In the first part, we present a construction of the stochastic integral of predictable square-integrable processes and the associated multiple stochastic integral...

Ogawa, Shigeyoshi Uemura, Hideaki
Published in
Bulletin des sciences mathématiques

Let Xt be a noncausal Itô process of Skorokhod type driven by the Brownian motion W., that is, a stochastic process of the form dXt=b(t,ω)dt+a(t,ω)dWt where the term a(⋅)dWt is understood as Skorokhod integral. For such an Itô process Xt we consider the Fourier coefficient Fn(dX) of the differential dXt by Fn(dX)=∫01en(t)¯dXt, en(t)=exp(2π−1nt) (n∈...

Liu, Da-Yan Gibaru, Olivier Perruquetti, Wilfrid

Recent algebraic parametric estimation techniques (see \cite{garnier,mfhsr}) led to point-wise derivative estimates by using only the iterated integral of a noisy observation signal (see \cite{num0,num}). In this paper, we extend such differentiation methods by providing a larger choice of parameters in these integrals: they can be reals. For this,...

Boudou, Alain Viguier-Pla, Sylvie

In this paper, we study how the locally concentration of the spectral measure expresses in the temporal domain for stationary processes. For this purpose, we establish an equivalence between the proximity of the shift operators (which are unit operators) and the associated projector-valued spectral measures. An illustration is given.

Garcia, Jorge
Published in
Journal of Theoretical Probability

Assuming that {(Xn,Yn)} satisfies the large deviation principle with good rate function I♯, conditions are given under which the sequence of triples {(Xn,Yn,Xn⋅Yn)} satisfies the large deviation principle. An ε-approximation to the stochastic integral is proven to be almost compact. As is well known from the contraction principle, we can derive the...

Bensoussan, Alain
Published in
Journal of Evolution Equations

Linear Random Functionals have been introduced by the author [2] to develop the theory of Kalman filtering for infinite dimensional linear systems. It is reminiscent of the concept of stochastic integral, which it partly generalizes. We compare it to that of cylindrical Wiener processes, introduced by G. Da Prato- J. Zabczyk [4]. Like distributions...

Picard, Jean

A stochastic calculus similar to Malliavin's calculus is worked out for Brownian excursions. The analogue of the Malliavin derivative in this calculus is not a differential operator, but its adjoint is (like the Skorohod integral) an extension of the Itô integral. As an application, we obtain an expression for the integrand in the stochastic integr...

Jones, Matthew O.

Committee Chair: Serfozo, Richard F.; Committee Member: Alexopoulos, Christos; Committee Member: Goldsman, David; Committee Member: Kertz, Robert; Committee Member: Shapiro, Alexander