484 research outputs found
Oscillating waves and optimal smoothing effect for one-dimensional nonlinear scalar conservation laws
Lions, Perthame, Tadmor conjectured in 1994 an optimal smoothing effect for
entropy solutions of nonlinear scalar conservations laws . In this short paper
we will restrict our attention to the simpler one-dimensional case. First,
supercritical geometric optics lead to sequences of solutions
uniformly bounded in the Sobolev space conjectured. Second we give continuous
solutions which belong exactly to the suitable Sobolev space. In order to do so
we give two new definitions of nonlinear flux and we introduce fractional
spaces
On the asymptotic expansion of the solutions of the separated nonlinear Schroedinger equation
Nonlinear Schr\"odinger equation (with the Schwarzian initial data) is
important in nonlinear optics, Bose condensation and in the theory of strongly
correlated electrons. The asymptotic solutions in the region ,
, can be represented as a double series in and .
Our current purpose is the description of the asymptotics of the coefficients
of the series.Comment: 11 pages, LaTe
On non-existence of a one factor interest rate model for volatility averaged generalized Fong-Vasicek term structures
The purpose of this paper is to study the generalized Fong--Vasicek
two-factor interest rate model with stochastic volatility. In this model the
dispersion of the stochastic short rate (square of volatility) is assumed to be
stochastic as well and it follows a non-negative process with volatility
proportional to the square root of dispersion. The drift of the stochastic
process for the dispersion is assumed to be in a rather general form including,
in particular, linear function having one root (yielding the original
Fong--Vasicek model or a cubic like function having three roots (yielding a
generalized Fong--Vasicek model for description of the volatility clustering).
We consider averaged bond prices with respect to the limiting distribution of
stochastic dispersion. The averaged bond prices depend on time and current
level of the short rate like it is the case in many popular one-factor interest
rate model including in particular the Vasicek and Cox--Ingersoll-Ross model.
However, as a main result of this paper we show that there is no such
one-factor model yielding the same bond prices as the averaged values described
above
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