Mixed-type stochastic differential equations driven by standard and fractional Brownian motions with Hurst indices greater than 1/3
https://doi.org/10.29235/1561-2430-2020-56-1-36-50
Abstract
In this paper we consider mixed-type stochastic differential equations driven by standard and fractional Brownian motions with Hurst indices greater than 1/3. There are proved theorems on the existence, uniqueness, and continuous dependence of solutions on the initial data. We provide an analog of the Ito formula to change variables. Asymptotic expansions of functionals on the solutions of mixed-type stochastic differential equations for small times are obtained. We receive analogs of the Kolmogorov equations for mathematical expectations and probability densities in the commutative case. Finally, we consider an application of mixed-type stochastic differential equations to solving the problem of macroeconomic variables extrapolation in credit risks models.
About the Author
M. M. Vas’kovskii
Belarusian State University
Belarus
Belarus
Maksim M. Vas’kovskii – Ph. D. (Physics and Mathematics), Associate Professor of the Department of Higher Mathematics, Belarusian State University
4, Nezavisimosti Ave., 220072, Minsk
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