III. Lévy flights 9 A. Underlying random walk process 9 B. Propagator and symmetries 10 C. Presence of external potentials 12 1. Harmonic potential 12 2. Steeper than harmonic potentials 13 D. First passage and first arrival of Lévy flights 15 E. Leapover properties of Lévy flights 17 F. Kramers problem for Lévy flights 18 G. More on the ”pathology” 20 H. Bi-fractional transport equations 22 I....

In this paper the problem of European option valuation in a Levy process setting is analysed. In our model the underlying asset follows a geometric Levy process. The jump part of the log-price process, which is a linear combination of Poisson processes, describes upward and downward jumps in price. The proposed pricing method is based on stochastic analysis and the theory of fuzzy sets. We assu...

We propose the model, which allows us to approximate fractional Levy noise and fractional Levy motion. Our model is based (i) on the Gnedenko limit theorem for an attraction basin of stable probability law, and (ii) on regarding fractional noise as the result of fractional integration/differentiation of a white Levy noise. We investigate self-affine properties of the approximation and conclude ...

We propose a new meta-heuristic algorithm named Levy flights multi-verse optimizer (LFMVO), which incorporates Levy flights into multi-verse optimizer (MVO) algorithm to solve numerical and engineering optimization problems. The Original MVO easily falls into stagnation when wormholes stochastically re-span a number of universes (solutions) around the best universe achieved over the course of i...

Levy and Levy (Management Science 2002) present data that, according to their claims, violate prospect theory. They suggest that prospect theory’s hypothesis of an S-shaped value function, concave for gains and convex for losses, is incorrect. However, all the data of Levy and Levy are perfectly consistent with the predictions of prospect theory, as can be verified by simply applying prospect t...

15. Olive, C., Geroch, M. E. & Levy, H. R. ( 197 1 ) J. Biol. Chem. 246,2047-2057 Levy, H. R. & Daouk, G. H. (1979) J. Biol. Chem. 254, 4843-4847 Grove, T. H., Ishaque, A. & Levy, H. R. ( I 976) Arch. Biochem. Biophys. 177,307-316 Levy, H. R., Christoff, M., Ingulli, J. & Ho, E. M. L. ( 1 983) Arch. Biochem. Biophys. 222,473-488 Levy, H. R.. Daouk, G. H. & Katopes, M. A. (1979) Arch. Riochem. B...

In this paper, we combine particle swarm optimization (PSO) and levy flight to solve the problem of protein folding prediction, which is based on 3D AB offlattice model. PSO has slow convergence speed and low precision in its late period, so we introduce levy flight into it to improve the precision and enhance the capability of jumping out of the local optima through particle mutation mechanism...