Displaying similar documents to “On the global maximum of the solution to a stochastic heat equation with compact-support initial data”

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...

Simulation and approximation of Lévy-driven stochastic differential equations

Nicolas Fournier (2011)

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 neglecting...

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...

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 ( ...