Displaying similar documents to “Simulation and approximation of Lévy-driven stochastic differential equations”

Adding constraints to BSDEs with jumps: an alternative to multidimensional reflections

Romuald Elie, Idris Kharroubi (2014)

ESAIM: Probability and Statistics

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This paper is dedicated to the analysis of backward stochastic differential equations (BSDEs) with jumps, subject to an additional global constraint involving all the components of the solution. We study the existence and uniqueness of a minimal solution for these so-called constrained BSDEs with jumps a penalization procedure. This new type of BSDE offers a nice and practical unifying framework to the notions of constrained BSDEs presented in [S. Peng and M. Xu, (2007)] and BSDEs with...

Survival probabilities of autoregressive processes

Christoph Baumgarten (2014)

ESAIM: Probability and Statistics

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Given an autoregressive process of order (  =   + ··· +   +  where the random variables , ,... are i.i.d.), we study the asymptotic behaviour of the probability that the process does not exceed a constant barrier up to time (survival or persistence probability). Depending on the coefficients ,...,...

Means in complete manifolds: uniqueness and approximation

Marc Arnaudon, Laurent Miclo (2014)

ESAIM: Probability and Statistics

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Let be a complete Riemannian manifold,  ∈ ℕ and  ≥ 1. We prove that almost everywhere on  = ( ,, ) ∈  for Lebesgue measure in , the measure μ ( x ) = N ∑ k = 1 N x k μ ( x ) = 1 N ∑ k = 1 N δ x k has a unique–mean (). As a consequence, if  = ( ,, ) is a -valued random variable with absolutely continuous law, then almost surely (()) has a unique –mean. In particular if ( ...

Simulation and approximation of Lévy-driven stochastic differential equations

Nicolas Fournier (2012)

ESAIM: Probability and Statistics

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We consider the approximate Euler scheme for Lévy-driven stochastic differential equations. We study the rate of convergence in law of the paths. We show that when approximating the small jumps by Gaussian variables, the convergence is much faster than when simply neglecting them. For example, when the Lévy measure of the driving process behaves like ||d near , for some (1,2), we obtain an error of order 1/√ with a computational cost of order . For a similar error when...

Hydrodynamic limit of a d-dimensional exclusion process with conductances

Fábio Júlio Valentim (2012)

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

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Fix a polynomial of the form () = + ∑2≤≤    =1 with (1) gt; 0. We prove that the evolution, on the diffusive scale, of the empirical density of exclusion processes on 𝕋 d , with conductances given by special class of functions, is described by the unique weak solution of the non-linear parabolic partial differential equation = ∑    ...

Local asymptotic normality for normal inverse gaussian Lévy processes with high-frequency sampling

Reiichiro Kawai, Hiroki Masuda (2013)

ESAIM: Probability and Statistics

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We prove the local asymptotic normality for the full parameters of the normal inverse Gaussian Lévy process , when we observe high-frequency data , ,, with sampling mesh  → 0 and the terminal sampling time  → ∞. The rate of convergence turns out to be (√, √, √, √) for the dominating parameter (), where stands for the heaviness of the tails, the degree of skewness, the scale, and the location. The essential feature in...

Pointwise constrained radially increasing minimizers in the quasi-scalar calculus of variations

Luís Balsa Bicho, António Ornelas (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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We prove of vector minimizers () =  (||) to multiple integrals ∫ ((), |()|)  on a  ⊂ ℝ, among the Sobolev functions (·) in + (, ℝ), using a  : ℝ×ℝ → [0,∞] with (·) and . Besides such basic hypotheses, (·,·) is assumed to satisfy also...

Nonparametric inference for discretely sampled Lévy processes

Shota Gugushvili (2012)

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

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Given a sample from a discretely observed Lévy process = ( )≥0 of the finite jump activity, the problem of nonparametric estimation of the Lévy density corresponding to the process is studied. An estimator of is proposed that is based on a suitable inversion of the Lévy–Khintchine formula and a plug-in device. The main results of the paper deal with upper risk bounds for estimation of over suitable classes of Lévy triplets. The corresponding lower bounds are also...

Wiener integral for the coordinate process under the σ-finite measure unifying brownian penalisations

Kouji Yano (2011)

ESAIM: Probability and Statistics

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Wiener integral for the coordinate process is defined under the -finite measure unifying Brownian penalisations, which has been introduced by [Najnudel , 345 (2007) 459–466] and [Najnudel , 19. Mathematical Society of Japan, Tokyo (2009)]. Its decomposition before and after last exit time from 0 is studied. This study prepares for the author's recent study [K. Yano, 258 (2010) 3492–3516] of Cameron-Martin formula for the -finite measure.