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Displaying 61 –
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666
In this paper we present a result on convergence of approximate solutions of stochastic differential equations involving integrals with respect to α-stable Lévy motion. We prove an appropriate weak limit theorem, which does not follow from known results on stability properties of stochastic differential equations driven by semimartingales. It assures convergence in law in the Skorokhod topology of sequences of approximate solutions and justifies discrete time schemes applied in computer simulations....
We establish some error estimates for the approximation of an optimal stopping problem along the paths of the Black–Scholes model. This approximation is based on a tree method. Moreover, we give a global approximation result for the related obstacle problem.
We establish some error estimates for the approximation of an
optimal stopping problem along the paths of the Black–Scholes
model. This approximation is based on a tree method. Moreover, we
give a global approximation result for the related obstacle
problem.
Let be a Lévy process started at , with Lévy measure . We consider the first passage time of to level , and the overshoot and the undershoot. We first prove that the Laplace transform of the random triple satisfies some kind of integral equation. Second, assuming that admits exponential moments, we show that converges in distribution as , where denotes a suitable renormalization of .
Let (Xt, t ≥ 0) be a Lévy process started at 0, with Lévy
measure ν. We consider the first passage time Tx of
(Xt, t ≥ 0) to level x > 0, and Kx := XTx - x the
overshoot and Lx := x- XTx- the undershoot. We first prove
that the Laplace transform of the random triple (Tx,Kx,Lx)
satisfies some kind of integral equation. Second, assuming that
ν admits exponential moments, we show that
converges in distribution as
x → ∞, where denotes a suitable
renormalization of Tx.
We study large deviations principles for N random processes on the lattice ℤd with finite time horizon [0, β] under a symmetrised measure where all initial and terminal points are uniformly averaged over random permutations. That is, given a permutation σ of N elements and a vector (x1, …, xN) of N initial points we let the random processes terminate in the points (xσ(1), …, xσ(N)) and then sum over all possible permutations and initial points, weighted with an initial distribution. We prove level-two...
Consider the group G:=PSL2(R) and its subgroups Γ:= PSL2(Z) and Γ':=DSL2(Z). G/Γ is a canonical realization (up to an homeomorphism) of the complement S3T of the trefoil knot T, and G/Γ' is a canonical realization of the 6-fold branched cyclic cover of S3T, which has a 3-dimensional cohomology of 1-forms.Putting natural left-invariant Riemannian metrics on G, it makes sense to ask which is the asymptotic homology performed by the Brownian motion in G/Γ', describing thereby in an intrinsic way part...
We consider a diffusion process smoothed with (small) sampling parameter . As in Berzin, León and Ortega (2001), we consider a kernel estimate with window of a function of its variance. In order to exhibit global tests of hypothesis, we derive here central limit theorems for the deviations such as
We consider a diffusion process Xt smoothed with (small)
sampling parameter ε. As in Berzin, León and Ortega
(2001), we consider a kernel estimate
with window h(ε) of a
function α of its variance. In order to exhibit global
tests of hypothesis, we derive here central limit theorems for
the Lp deviations such as
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666