Seminars of the Focus Area Complex Systems

Prof. Dr. C. Beta, Prof. Dr. K. Dethloff, Prof. Dr. R. Engbert, Prof. Dr. M. Holschneider, Prof. Dr. W. Huisinga, Prof. Dr. Ralf Metzler, Prof. Dr. A. Pikovsky, Prof. Dr. S. Reich, Prof. Dr. M. Rosenblum, Prof. Dr. G. Rüdiger, Prof. Dr. T. Scheffer, Prof. Dr. F. Scherbaum, Prof. Dr. J. Selbig, Prof. Dr. F. Spahn


Speaker: Ilya Pavlyukevich, Institute of Mathematics, Friedrich Schiller University Jena

Title: Marcus versus Stratonovich for systems with jump noise * Colloquium on Complex and Biological Systems

Time: Fri, Feb 20, 2015, 10:15am

Place: bldg 28, room 2.123

The famous Ito-Stratonovich dilemma arises when one examines a dynamical system with a multiplicative white noise. In physics literature, this dilemma is often resolved in favour of the Stratonovich prescription because of its two characteristic properties valid for systems driven by Brownian motion: (i) it allows physicists to treat stochastic integrals in the same way as conventional integrals, and (ii) it appears naturally as a result of a small correlation time limit procedure.
In this talk we will show that a naive application of the Stratonovich calculus for jump noises does not lead to the desired properties. Instead, the so-called Marcus prescription should be used.
We will present an in-depth comparison of the Ito, Stratonovich and Marcus equations for systems with multiplicative jump noise and consider illustrative examples of a real-valued linear system and a complex oscillator with noisy frequency (the Kubo-Anderson oscillator).
This talk is based on a recent joint paper with A. Chechkin (J. Phys. A: Math. Theor 47 (2014) 342001, Fast Track Communication)

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Udo Schwarz, Zentrum für Dynamik komplexer Systeme,
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