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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2010 Volume 384, Pages 238–266 (Mi znsl3894)

This article is cited in 4 papers

The probabilistic representation of the decisions of a class of evolution equations

N. V. Smorodina, M. M. Faddeev

St. Petersburg State University, Faculty of Physics, St. Petersburg, Russia

Abstract: We consider a class of pseudo-differential operators acting on test functions as a convolution with a given generalized function. For evolution families with generators from this class we construct an analog of a probabilistic representation. Bibl. 9 titles.

Key words and phrases: random measures, pseudo-process, evolution equation, generalized function.

UDC: 519.21

Received: 18.10.2010


 English version:
Journal of Mathematical Sciences (New York), 2011, 176:2, 239–254

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© Steklov Math. Inst. of RAS, 2025