arXiv subjects

Paul Raynaud de Fitte

Publications and source records attributed to Paul Raynaud de Fitte.

9 recordsLinked to original sources

arXiv2022

On a Set-Valued Young Integral with Applications to Differential Inclusions

We present a new Aumann-like integral for a Hölder multifunction with respect to a Hölder signal, based on the Young integral of a particular set of Hölder selections. This restricted Aumann integral has continuity properties that allow for numerical approximation as well as an existence theorem for an abstract stochastic differential inclusion. This is applied to concrete examples of first order and second order stochastic differential inclusions directed by fractional Brownian motion.

math.PR↗

arXiv2020

Almost periodicity and periodicity for nonautonomous random dynamical systems

We present a notion of almost periodicity wich can be applied to random dynamical systems as well as almost periodic stochastic differential equations in Hilbert spaces (abstract stochastic partial differential equations). This concept allows for improvements of known results of almost periodicity in distribution, for general random processes and for solutions to stochastic differential equations.

math.DS↗

arXiv2020

Almost Periodic and Periodic Solutions of Differential Equations Driven by the Fractional Brownian Motion with Statistical Application

We show that the unique solution to a semilinear stochastic differential equation with almost periodic coefficients driven by a fractional Brownian motion is almost periodic in a sense related to random dynamical systems. This type of almost periodicity allows for the construction of a consistent estimator of the drift parameter in the almost periodic and periodic cases.

math.PR↗

arXiv2019

Dynamics of a prey-predator system with modified Leslie-Gower and Holling type II schemes incorporating a prey refuge

We study a modified version of a prey-predator system with modified Leslie-Gower and Holling type II functional response studied by M.A. Aziz-Alaoui and M. Daher-Okiye. The modification consists in incorporating a refuge for preys, and substantially complicates the dynamics of the system. We study the local and global dynamics and the existence of cycles. We also investigate conditions for extinction or existence of a stationary distribution, in the case of a stochastic perturbation of the system.

math.PR↗

arXiv2018

Weyl almost periodic solutions to abstract linear and semilinear equations with Weyl almost periodic coefficients

In this work, we study the existence and uniqueness of bounded Weyl almost periodic solution to the abstract differential equation u ' (t) = Au(t) + f (t), t $\in$ R, in a Banach space X, where A : D (A) $\subset$ X $\rightarrow$ X is a linear operator (unbounded) which generates an exponentially stable C 0-semigroup on X and f : R $\rightarrow$ X is a Weyl almost periodic function. We also investigate the nonautonomous case.

math.PR↗

arXiv2017

Almost periodic solution in distribution for stochastic differential equations with Stepanov almost periodic coefficients

This paper deals with the existence and uniqueness of ($μ$-pseudo) almost periodic mild solution to some evolution equations with Stepanov ($μ$-pseudo) almost periodic coefficients, in both determinist and stochastic cases. After revisiting some known concepts and properties of Stepanov ($μ$-pseudo) almost periodicity in complete metric space, we consider a semilinear stochastic evolution equation on a Hilbert separable space with Stepanov ($μ$-pseudo) almost periodic coefficients. We show existence and uniqueness of the mild solution which is ($μ$-pseudo) almost periodic in 2-distribution. We also generalize a result by Andres and Pennequin, according to which there is no purely Stepanov almost periodic solutions to differential equations with Stepanov almost periodic coefficients.

math.PR↗

arXiv2017

Global stability of almost periodic solutions of monotone sweeping processes and their response to non-monotone perturbations

We develop a theory which allows making qualitative conclusions about the dynamics of both monotone and non-monotone Moreau sweeping processes. Specifically, we first prove that any sweeping processes with almost periodic monotone right-hand-sides admits a globally exponentially stable almost periodic solution. And then we describe the extent to which such a globally stable solution persists under non-monotone perturbations.

math.DS↗

arXiv2017

Weak Averaging of Semilinear Stochastic Differential Equations with Almost Periodic Coefficients

An averaging result is proved for stochastic evolution equations with highly oscillating coefficients. This result applies in particular to equations with almost periodic coefficients. The convergence to the solution of the averaged equation is obtained in distribution, as in previous works by Khasminskii and Vrko{\v c}.This version corrects two minor errors from our paper published in J. Math. Anal. Appl. 427(1):336--364, 2015.

math.PR↗

arXiv2015

Almost automorphy and various extensions for stochastic processes

We compare different modes of pseudo almost automorphy and variants for stochastic processes: in probability, in quadratic mean, or in distribution in various senses. We show by a counterexample that square-mean (pseudo) almost automorphy is a property which is too strong for stochastic differential equations (SDEs). Finally, we consider two semilinear SDEs, one with almost automorphic coefficients and the second one with pseudo almost automorphic coefficients, and we prove the existence and uniqueness of a mild solution which is almost automorphic in distribution in the first case, and pseudo almost automorphic in distribution in the second case.

math.PR↗