Abstract:
In the direct product of algebras of generalized random process, equations in differentials and their associated solutions are considered. It is proved that, in some cases, they are solutions of the corresponding Ito stochastic differential equations, and, in other cases, they are solutions of the Stratonovich equations.
Keywords:
stochastic differential equations, Ito and Stratonovich equations, direct product of algebrasof generalized random processes, Ito and Stratonovich generalized differentials, associated solutions of equations in differentials.
Citation:
N. V. Lazakovich, S. P. Stashulenok, T. V. Stemkovskaya, “Associated solutions of equations in differentialsin the direct product of algebras of generalized random processes”, Teor. Veroyatnost. i Primenen., 43:2 (1998), 272–293; Theory Probab. Appl., 43:2 (1999), 221–238
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\paper Associated solutions of equations in~differentialsin the direct product of algebras of generalized random processes
\jour Teor. Veroyatnost. i Primenen.
\yr 1998
\vol 43
\issue 2
\pages 272--293
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\transl
\jour Theory Probab. Appl.
\yr 1999
\vol 43
\issue 2
\pages 221--238
\crossref{https://doi.org/10.1137/S0040585X97976842}
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Linking options:
https://www.mathnet.ru/eng/tvp1465
https://doi.org/10.4213/tvp1465
https://www.mathnet.ru/eng/tvp/v43/i2/p272
This publication is cited in the following 2 articles:
A. N. Koval'chuk, O. L. Yablonskii, V. G. Navakhrost, “On the approximation of differential equations with generalized coefficients by finite-difference equations with averaging”, Russian Math. (Iz. VUZ), 49:3 (2005), 21–29
N. V. Lazakovich, O. L. Yablonskii, “Limit behavior of Ito finite sums with avaraging”, Theory Probab. Appl., 50:4 (2006), 612–630
Citation in format AMSBIB
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