All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 2 Next

Displaying 21 – 40 of 51

Showing per page

Ergodicity of hypoelliptic SDEs driven by fractional brownian motion

M. Hairer, N. S. Pillai (2011)

Annales de l'I.H.P. Probabilités et statistiques

We demonstrate that stochastic differential equations (SDEs) driven by fractional brownian motion with Hurst parameter H>½ have similar ergodic properties as SDEs driven by standard brownian motion. The focus in this article is on hypoelliptic systems satisfying Hörmander’s condition. We show that such systems enjoy a suitable version of the strong Feller property and we conclude that under a standard controllability condition they admit a unique stationary solution that is physical in the...

Estimation in models driven by fractional brownian motion

Corinne Berzin, José R. León (2008)

Annales de l'I.H.P. Probabilités et statistiques

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(⋅)...

Euler scheme for SDEs with non-Lipschitz diffusion coefficient : strong convergence

Abdel Berkaoui, Mireille Bossy, Awa Diop (2008)

ESAIM: Probability and Statistics

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 SDEs with non-Lipschitz diffusion coefficient: strong convergence

Abdel Berkaoui, Mireille Bossy, Awa Diop (2007)

ESAIM: Probability and Statistics

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.

Exact simulation for solutions of one-dimensional Stochastic Differential Equations with discontinuous drift

Pierre Étoré, Miguel Martinez (2014)

ESAIM: Probability and Statistics

In this note we propose an exact simulation algorithm for the solution of (1) d X t = d W t + b ¯ ( X t ) d t , X 0 = x , d X t = d W t + b̅ ( X t ) d t,   X 0 = x, where b ¯ b̅is a smooth real function except at point 0 where b ¯ ( 0 + ) ≠ b ¯ ( 0 - ) 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 + b ¯ ( X t β ) d t + β d L t 0 ( X β ) , X 0 = x 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...

Existence and asymptotic behaviour of some time-inhomogeneous diffusions

Mihai Gradinaru, Yoann Offret (2013)

Annales de l'I.H.P. Probabilités et statistiques

Let us consider a solution of a one-dimensional stochastic differential equation driven by a standard Brownian motion with time-inhomogeneous drift coefficient ρ sgn ( x ) | x | α / t β . 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 ρ , α and β , of the recurrence, transience and convergence. More precisely, asymptotic...

Currently displaying 21 – 40 of 51