Posashkova S. Stochastic differential equations with nonhomogeneous non-Lipschitz diffusion coefficient and mixed equations with fractional Brownian motion

Українська версія

Thesis for the degree of Candidate of Sciences (CSc)

State registration number

0414U001117

Thesis Registration Form

0414U001117.pdf

Applicant for

Specialization

  • 01.01.05 - Теорія ймовірностей і математична статистика

27-01-2014

Specialized Academic Board

Д 26.001.37

Taras Shevchenko National University of Kyiv

Essay

The thesis is devoted to models driven by Wiener process and fractional Brownian motion. Sufficient conditions on the coefficients to ensure positivity for trajectories of solution of the stochastic differential equations with nonhomogeneous coefficients and non-Lipschitz diffusion coefficient are established. Euler approximation scheme is constructed and the rate of convergence of approximations to the solution is found. The limit behavior with respect to a parameter for solutions of equations driven by Wiener process and fractional Brownian motion is investigated.

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Files

aref.pdf

dis.pdf

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