9,827 research outputs found
Dynamic risk measures on variable exponent Bochner--Lebesgue spaces
In this paper, we will study several classes of risk measures on a special
space where the variable exponent is no longer a
given real number like the space , but a random variable, which reflects
the possible volatility of the financial markets. The dual representations for
them are also provided
Self-Organized Cooperative Criticality in Coupled Complex Systems
We show that the coupled complex systems can evolve into a new kind of
self-organized critical state where each subsystem is not critical, however,
they cooperate to be critical. This criticality is different from the classical
BTW criticality where the single system itself evolves into a critical state.
We also find that the outflows can be accumulated in the coupled systems. This
will lead to the emergency of spatiotemporal intermittency in the critical
state
Convergence of densities of some functionals of Gaussian processes
The aim of this paper is to establish the uniform convergence of the
densities of a sequence of random variables, which are functionals of an
underlying Gaussian process, to a normal density. Precise estimates for the
uniform distance are derived by using the techniques of Malliavin calculus,
combined with Stein's method for normal approximation. We need to assume some
non-degeneracy conditions. First, the study is focused on random variables in a
fixed Wiener chaos, and later, the results are extended to the uniform
convergence of the derivatives of the densities and to the case of random
vectors in some fixed chaos, which are uniformly non-degenerate in the sense of
Malliavin calculus. Explicit upper bounds for the uniform norm are obtained for
random variables in the second Wiener chaos, and an application to the
convergence of densities of the least square estimator for the drift parameter
in Ornstein-Uhlenbeck processes is discussed
Feynman--Kac formula for the heat equation driven by fractional noise with Hurst parameter
In this paper, a Feynman-Kac formula is established for stochastic partial
differential equation driven by Gaussian noise which is, with respect to time,
a fractional Brownian motion with Hurst parameter . To establish such a
formula, we introduce and study a nonlinear stochastic integral from the given
Gaussian noise. To show the Feynman--Kac integral exists, one still needs to
show the exponential integrability of nonlinear stochastic integral. Then, the
approach of approximation with techniques from Malliavin calculus is used to
show that the Feynman-Kac integral is the weak solution to the stochastic
partial differential equation.Comment: Published in at http://dx.doi.org/10.1214/11-AOP649 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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