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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2010 Volume 384, Pages 78–104 (Mi znsl3886)

Distributions of functionals of diffusions with jumps connected with the location of the maximum or minimum

A. N. Borodin

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia

Abstract: The paper deals with methods of computations of distributions of integral functionals of diffusions with jumps at the time moments, in which the maximum and the minimum values of diffusions are achieved. As an example an explicit formulas for the Laplace transform of joint locations of minimum and maximum of the process equal the sum of Brownian motion and the compound Poisson process are obtained. Bibl. 7 titles.

Key words and phrases: distribution of functionals, diffusion with jumps, location of minimum, location of maximum.

UDC: 519

Received: 30.10.2010


 English version:
Journal of Mathematical Sciences (New York), 2011, 176:2, 146–161

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© Steklov Math. Inst. of RAS, 2024