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Itô vs Stratonovich in the presence of absorbing states
Stockholm University, Faculty of Science, Department of Mathematics. Universidad Autónoma de Madrid, Spain.
Number of Authors: 22019 (English)In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 60, no 12, article id 123301Article in journal (Refereed) Published
Abstract [en]

It is widely assumed that there exists a simple transformation from the Ito interpretation to the one by Stratonovich and back for any stochastic differential equation of applied interest. While this transformation exists under suitable conditions, and transforms one interpretation into the other at the price of modifying the drift of the equation, it cannot be considered universal. We show that a class of stochastic differential equations, characterized by the presence of absorbing states and of interest in applications, does not admit such a transformation. In particular, formally applying this transformation may lead to the disappearance of some absorbing states. In turn, this modifies the long-time, and even the intermediate-time, behavior of the solutions. The number of solutions can also be modified by the unjustified application of the mentioned transformation, as well as by a change in the interpretation of the noise. We discuss how these facts affect the classical debate on the Itô vs Stratonovich dilemma.

Place, publisher, year, edition, pages
2019. Vol. 60, no 12, article id 123301
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-178712DOI: 10.1063/1.5081791ISI: 000505527100001OAI: oai:DiVA.org:su-178712DiVA, id: diva2:1402241
Available from: 2020-02-28 Created: 2020-02-28 Last updated: 2020-02-28Bibliographically approved

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