We propose a simple model based on the Gnedenko limit theorem for simulation and studies of the ordinary Levy motion, that is, a random process, whose increments are independent and distributed with a stable probability law. We use the generalized structure function for characterizing anomalous diffusion rate and propose to explore the modified Hurst method for empirical rescaled range analysis...

We consider the numerical solution of one type integro-differential equation by a probability method based on fundamental martingale mixed Gaussian processes. As an application, we try to simulate estimation ruin with an unknown parameter driven not classical Levy process, but fractional Brownian motion.

Along an individual lifetime, stem cells replicate and suffer modifications in their DNA content. I model the modifications in the DNA of a single cell as a Levy flight, made up of small amplitude Brownian motions plus rare large-jumps events. The distribution function of mutations has a long tail, in which cancer events are located far away. The probability of cancer in a given tissue is rough...

This paper revisits Levy sections theorem, which generalizes the central limit theorem to encompass autocorrelated variables. Levy sections theorem’s approach is extended to time series and applied to historical daily returns of selected dollar exchange rates. We explain the elevated kurtosis usually observed in such series by their volatilities. In particular, the high kurtosis of emerging mar...

Azriel Levy (1934–) did fundamental work in set theory when it was transmuting into a modern, sophisticated field of mathematics, a formative period of over a decade straddling Cohen’s 1963 founding of forcing. The terms “Levy collapse”, “Levy hierarchy”, and “Levy absoluteness” will live on in set theory, and his technique of relative constructibility and connections established between forcin...

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Title of dissertation: DEPENDENCE STRUCTURE IN LEVY PROCESSES AND ITS APPLICATION IN FINANCE Qiwen Chen, Doctor of Philosophy, 2008 Dissertation directed by: Professor Dilip B. Madan Department of Finance In this paper, we introduce DSPMD, discretely sampled process with prespecified marginals and pre-specified dependence, and SRLMD, series representation for Levy process with pre-specified mar...

In recent studies the truncated Levy process (TLP) has been shown to be very promising for the modeling of financial dynamics. In contrast to the Levy process, the TLP has finite moments and can account for both the previously observed excess kurtosis at short timescales, along with the slow convergence to Gaussian at longer timescales. In this paper I further test the truncated Levy paradigm u...

We develop Bayesian Markov chain Monte Carlo methods for inferences of continuoustime models with stochastic volatility and infinite-activity Levy jumps using discretely sampled data. Simulation studies show that (i) our methods provide accurate joint identification of diffusion, stochastic volatility, and Levy jumps, and (ii) affine jumpdiffusion models fail to adequately approximate the behav...