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Displaying 441 –
460 of
472
The EGARCH model of Nelson [29] is one of the most successful ARCH models which may exhibit characteristic asymmetries of financial time series, as well as long memory. The paper studies the covariance structure and dependence properties of the EGARCH and some related stochastic volatility models. We show that the large time behavior of the covariance of powers of the (observed) ARCH process is determined by the behavior of the covariance of the (linear) log-volatility process; in particular, a...
The EGARCH model of Nelson [29] is one of the most
successful
ARCH models which may exhibit characteristic asymmetries of
financial time series, as well as long memory. The paper studies
the covariance structure and dependence properties of the EGARCH
and some related stochastic volatility models. We show that the
large time behavior of the covariance of powers of the (observed)
ARCH process is determined by the behavior of the covariance of
the (linear) log-volatility process; in particular,...
Let be a locally compact non-compact metric group. Assuming that is abelian we construct symmetric aperiodic random walks on with probabilities of return to any neighborhood V of the neutral element decaying at infinity almost as fast as the exponential function n ↦ exp(-n). We also show that for some discrete groups , the decay of the function can be made as slow as possible by choosing appropriate aperiodic random walks Sₙ on .
In this paper, we are interested in a diffusion process based on a gradient descent. The process is non Markov and has a memory term which is built as a weighted average of the drift term all along the past of the trajectory. For this type of diffusion, we study the long time behaviour of the process in terms of the memory. We exhibit some conditions for the long-time stability of the dynamical system and then provide, when stable, some convergence properties of the occupation measures and of the...
We consider a long-range version of self-avoiding walk in dimension d > 2(α ∧ 2), where d denotes dimension and α the power-law decay exponent of the coupling function. Under appropriate scaling we prove convergence to brownian motion for α ≥ 2, and to α-stable Lévy motion for α < 2. This complements results by Slade [J. Phys. A21 (1988) L417–L420], who proves convergence to brownian motion for nearest-neighbor self-avoiding walk in high dimension.
Given the probability measure over the given region , we consider the optimal location of a set composed by points in in order to minimize the average distance (the classical optimal facility location problem). The paper compares two strategies to find optimal configurations: the long-term one which consists in placing all points at once in an optimal position, and the short-term one which consists in placing the points one by one adding at each step at most one point and preserving...
Given the probability measure ν over the given region
, we consider the optimal location of a set
Σ composed by n points in Ω in order to minimize the
average distance (the
classical optimal facility location problem). The paper compares two
strategies to find optimal configurations: the long-term one which
consists in
placing all n points at once in an optimal position, and the
short-term one which consists in placing the points one by one adding
at each step at most one point and preserving...
We show that any loop-free Markov chain on a discrete space can be viewed as a determinantal point process. As an application, we prove central limit theorems for the number of particles in a window for renewal processes and Markov renewal processes with Bernoulli noise.
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