Mixed stochastic differential equations with long-range dependence: Existence, uniqueness and convergence of solutions

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• 作者：Yuliya Mishura ^{myus@univ.kiev.ua} ; Georgiy Shevchenko ; ^{zhora@univ.kiev.ua}
• 关键词：Mixed stochastic differential equation ; Pathwise integral ; Long-range dependence ; Fractional Brownian motion ; Stochastic differential equation with random drift
• 刊名：Computers and Mathematics with Applications
• 出版年：2012
• 出版时间：November, 2012
• 年：2012
• 卷：64
• 期：10
• 页码：3217-3227
• 全文大小：256 K

文摘

For a mixed stochastic differential equation involving standard Brownian motion and an almost surely H?lder continuous process with H?lder exponent , we establish a new result on its unique solvability. We also establish an estimate for difference of solutions to such equations with different processes and deduce a corresponding limit theorem. As a by-product, we obtain a result on existence of moments of a solution to a mixed equation under an assumption that has certain exponential moments.