13,500 research outputs found
On sequences of projections of the cubic lattice
In this paper we study sequences of lattices which are, up to similarity,
projections of onto a hyperplane , with
and converge to a target lattice which
is equivalent to an integer lattice. We show a sufficient condition to
construct sequences converging at rate and exhibit
explicit constructions for some important families of lattices.Comment: 16 pages, 5 figure
Central limit theorems for additive functionals of ergodic Markov diffusions processes
We revisit functional central limit theorems for additive functionals of
ergodic Markov diffusion processes. Translated in the language of partial
differential equations of evolution, they appear as diffusion limits in the
asymptotic analysis of Fokker-Planck type equations. We focus on the square
integrable framework, and we provide tractable conditions on the infinitesimal
generator, including degenerate or anomalously slow diffusions. We take
advantage on recent developments in the study of the trend to the equilibrium
of ergodic diffusions. We discuss examples and formulate open problems
Quadratic BSDEs driven by a continuous martingale and application to utility maximization problem
In this paper, we study a class of quadratic Backward Stochastic Differential
Equations (BSDEs) which arises naturally when studying the problem of utility
maximization with portfolio constraints. We first establish existence and
uniqueness results for such BSDEs and then, we give an application to the
utility maximization problem. Three cases of utility functions will be
discussed: the exponential, power and logarithmic ones
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