1,934 research outputs found
Pathwise optimal transport bounds between a one-dimensional diffusion and its Euler scheme
In the present paper, we prove that the Wasserstein distance on the space of
continuous sample-paths equipped with the supremum norm between the laws of a
uniformly elliptic one-dimensional diffusion process and its Euler
discretization with steps is smaller than where
is an arbitrary positive constant. This rate is intermediate
between the strong error estimation in obtained when coupling the
stochastic differential equation and the Euler scheme with the same Brownian
motion and the weak error estimation obtained when comparing the
expectations of the same function of the diffusion and of the Euler scheme at
the terminal time . We also check that the supremum over of the
Wasserstein distance on the space of probability measures on the real line
between the laws of the diffusion at time and the Euler scheme at time
behaves like .Comment: Published in at http://dx.doi.org/10.1214/13-AAP941 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Gaussian-type lower bounds for the density of solutions of SDEs driven by fractional Brownian motions
In this paper we obtain Gaussian-type lower bounds for the density of
solutions to stochastic differential equations (SDEs) driven by a fractional
Brownian motion with Hurst parameter . In the one-dimensional case with
additive noise, our study encompasses all parameters , while the
multidimensional case is restricted to the case . We rely on a mix of
pathwise methods for stochastic differential equations and stochastic analysis
tools.Comment: Published at http://dx.doi.org/10.1214/14-AOP977 in the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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Testes de progênie de Pinus elliottii de polinização livre.
bitstream/item/101193/1/PA-1983-Higa-TestesProgenise.pd
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