680 citations · 965 across the 33 of their papers we have counts for
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First passage properties of asymmetric Lévy flights
A. Padash, A. V. Chechkin, B. Dybiec +3
Lévy Flights are paradigmatic generalised random walk processes, in which the independent stationary increments---the "jump lengths"---are drawn from an -stable jump length dist…
Marcus versus Stratonovich for Systems with Jump Noise
Alexei Chechkin, Ilya Pavlyukevich
The famous Itô-Stratonovich dilemma arises when one examines a dynamical system with a multiplicative white noise. In physics literature, this dilemma is often resolved in favour o…
Lévy Ratchet in a Weak Noise Limit: Theory and Simulation
Ilya Pavlyukevich, Bartlomiej Dybiec, Aleksei V. Chechkin +1
We study the motion of a particle embedded in a time independent periodic potential with broken mirror symmetry and subjected to a Lévy noise possessing Lévy stable probability law…
Levy Flights, Non-local Search and Simulated Annealing
I. Pavlyukevich
We solve a problem of non-convex stochastic optimisation with help of simulated annealing of Levy flights of a variable stability index. The search of the ground state of an unknow…
Cooling down Levy flights
I. Pavlyukevich
Let L(t) be a Levy flights process with a stability index α\in(0,2), and U be an external multi-well potential. A jump-diffusion Z satisfying a stochastic differential equation dZ(…