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Asymptotic behavior of the martingale type integral functionals for unstable solutions to stochastic differential equations

G. L. KulinichSvitlana KushnirenkoORCIDYuliya MishuraORCID

Анотація

We consider functionals of the type $\int _ {0} ^ {t} g (\xi (s)) dW (s)$, $t \ge 0$. Here $g$ is a real valued and locally square integrable function, $\xi$ is a unique strong solution of the Itô stochastic differential equation $d \xi (t) = a (\xi (t)) dt + dW (t)$, $a$ is a measurable real valued bounded function such that $| xa (x) | \le C$. The behavior of these functionals is studied as $t \to \infty$. The appropriate normalizing factor and the explicit form of the limit random variable are established.

Класифікація

Домен
Physical SciencesSocial Sciences
Галузь
Computer ScienceEconomics, Econometrics and FinanceEngineering
Підгалузь
Computational Theory and MathematicsFinanceControl and Systems Engineering
Тема
Advanced Mathematical Modeling in Engineering★Stochastic processes and financial applicationsStability and Controllability of Differential Equations

Ідентифікатори

DOI: 10.1090/tpms/953

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