Results 271 to 280 of about 18,649,447 (327)

Efficient estimation of stable Lévy process with symmetric jumps

Statistical Inference for Stochastic Processes : An International Journal devoted to Time Series Analysis and the Statistics of Continuous Time Processes and Dynamical Systems, 2018
Efficient estimation of a non-Gaussian stable Lévy process with drift and symmetric jumps observed at high frequency is considered. For this statistical experiment, the local asymptotic normality of the likelihood is proved with a non-singular Fisher ...
A. Brouste, Hiroki Masuda
semanticscholar   +1 more source

Exponential Stability of Solutions to Stochastic Differential Equations Driven by G-Lévy Process

Applied Mathematics and Optimization, 2018
In this paper, BDG-type inequality for G-stochastic calculus with respect to G-Lévy process is obtained, and solutions of the stochastic differential equations driven by the G-Lévy process under the non-Lipschitz condition are constructed.
Bingjun Wang, Hongjun Gao
semanticscholar   +1 more source

Option Pricing with Levy Process [PDF]

SSRN Electronic Journal, 2001
In this paper, we assume that log returns can be modelled by a Levy process. We give explicit formulae for option prices by means of the Fourier transform. We explain how to infer the characteristics of the Levy process from option prices. This enables us to generate an implicit volatility surface implied by market data.
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Levy processes for image modeling

Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics. SPW-HOS '99, 2003
Nonhomogenous random fields are known to be well adapted to modeling a wide class of images. Their computational complexity generally causes their lack of appeal, we propose a more efficient model capable of capturing textures, shapes, as well as jumps typically encountered in infra-red images.
O.V. Poliannikov, null Yufang Bao, H. Krim   +2 more
openaire   +1 more source

Functionals of a Lévy Process on Canonical and Generic Probability Spaces

, 2013
We develop an approach to Malliavin calculus for Lévy processes from the perspective of expressing a random variable $$Y$$Y by a functional $$F$$F mapping from the Skorohod space of càdlàg functions to $$\mathbb {R}$$R, such that $$Y=F(X)$$Y=F(X) where $$
Alexander Steinicke
semanticscholar   +1 more source

A geometric interpretation of the transition density of a symmetric Lévy process

, 2011
We study for a class of symmetric Lévy processes with state space ℝn the transition density pt (x) in terms of two one-parameter families of metrics, (dt)t>0 and (δt)t>0.
N. Jacob, Victorya Knopova, S. Landwehr, R. Schilling   +3 more
semanticscholar   +1 more source

Finite-size Lyapunov exponent for Levy processes

Physical Review E, 2007
The finite-size Lyapunov exponent (FSLE) is the exponential rate at which two particles separate from a distance of r to a x r (a>1) and provides a measure of dispersive mixing in chaotic systems. It is shown analytically that for particle trajectories governed by symmetric alpha -stable Levy motion, the FSLE is proportional to the diffusion ...
R, Parashar, J H, Cushman
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Mean Reverting Levy Based Processes

SSRN Electronic Journal, 2012
We investigate Stochastic Processes that are mean reverting (and have leptokurtic distributions. A new MR process is proposed which utilizes the infinitely divisible property of Levy process. The process itself can be calibrated and simulated easily using a small number of discrete time steps.
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Fast Simulation of Levy Processes

SSRN Electronic Journal, 2012
We present a robust method for simulating an increment of a Levy process, based on decomposing the jump part of the process into the sum of its positive and negative jump components. The characteristic exponent of a spectrally one-sided Levy process has excellent analytic properties, which we exploit to design a fast and accurate algorithm for ...
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On Levy's area process

2006
We prove a law of the iterated logarithm for the Euclidean norm of a particulan vecton process in ℝ3 and give formulae for its characteristic and conditional characteristic functions. The conditional characteristic function yields an explicit expression for the propagaton of the Schrodinger operaton with constant magnetic field.
openaire   +1 more source