Estimates for the derivative of diffusion semigroups.
Estimation dans de la loi de certains processus à accroissements indépendants
Estimation in models driven by fractional brownian motion
Let {bH(t), t∈ℝ} be the fractional brownian motion with parameter 0<H<1. When 1/2<H, we consider diffusion equations of the type X(t)=c+∫0tσ(X(u)) dbH(u)+∫0tμ(X(u)) du. In different particular models where σ(x)=σ or σ(x)=σ x and μ(x)=μ or μ(x)=μ x, we propose a central limit theorem for estimators of H and of σ based on regression methods. Then we give tests of the hypothesis on σ for these models. We also consider functional estimation on σ(⋅)...
Estimations de grandes déviations pour des systèmes où apparaissent un bruit Gaussien et un bruit non Gaussien
Étude d'une équation différentielle stochastique avec temps local
Étude d'une fonctionnelle liée au pont de Bessel
Euler scheme for SDEs with non-Lipschitz diffusion coefficient : strong convergence
We consider one-dimensional stochastic differential equations in the particular case of diffusion coefficient functions of the form , . In that case, we study the rate of convergence of a symmetrized version of the Euler scheme. This symmetrized version is easy to simulate on a computer. We prove its strong convergence and obtain the same rate of convergence as when the coefficients are Lipschitz.
Euler scheme for SDEs with non-Lipschitz diffusion coefficient: strong convergence
We consider one-dimensional stochastic differential equations in the particular case of diffusion coefficient functions of the form |x|α, α ∈ [1/2,1). In that case, we study the rate of convergence of a symmetrized version of the Euler scheme. This symmetrized version is easy to simulate on a computer. We prove its strong convergence and obtain the same rate of convergence as when the coefficients are Lipschitz.
Euler scheme for solutions of stochastic differential equations with non-Lipschitz coefficients.
Euler-Maruyama approximations in mean-reverting stochastic volatility model under regime-switching.
Évolution d'une file d'attente avec priorité
Evolution in random environment and structural instability.
Exact simulation for solutions of one-dimensional Stochastic Differential Equations with discontinuous drift
In this note we propose an exact simulation algorithm for the solution of (1)d X t = d W t + b̅ ( X t ) d t, X 0 = x, where b̅is a smooth real function except at point 0 where b̅(0 + ) ≠ b̅(0 −) . The main idea is to sample an exact skeleton of Xusing an algorithm deduced from the convergence of the solutions of the skew perturbed equation (2)d X t β = d W t + b̅ ( X t β ) d t + β d L t 0 ( X β ) , X 0 = x towardsX solution of (1) as β ≠ 0 tends to 0. In this note, we show that this convergence...
Excercises in stochastic analysis
Existence and asymptotic behaviour of some time-inhomogeneous diffusions
Let us consider a solution of a one-dimensional stochastic differential equation driven by a standard Brownian motion with time-inhomogeneous drift coefficient . This process can be viewed as a Brownian motion evolving in a potential, possibly singular, depending on time. We prove results on the existence and uniqueness of solution, study its asymptotic behaviour and made a precise description, in terms of parameters , and , of the recurrence, transience and convergence. More precisely, asymptotic...
Existence and stability of solutions for nonautonomous stochastic functional evolution equations.
Existence and uniqueness of solutions for BSDEs with locally Lipschitz coefficient.
Existence et unicité de diffusions à valeurs dans un espace de Hilbert
Existence of quadratic-mean almost periodic solutions to some stochastic hyperbolic differential equations.
Existence of -almost periodic solutions to a class of nonautonomous stochastic evolution equations.