Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

existence and measurability of the solution of the stochastic differential equations driven by fractional brownian motion

existence and approximate $l^{p}$ and continuous solution of nonlinear integral equations of the hammerstein and volterra types

بسیاری از پدیده ها در جهان ما اساساً غیرخطی هستند، و توسط معادلات غیرخطی ‎‏بیان شد‎‎‏ه اند. از آنجا که ظهور کامپیوترهای رقمی با عملکرد بالا، حل مسایل خطی را آسان تر می کند. با این حال، به طور کلی به دست آوردن جوابهای دقیق از مسایل غیرخطی دشوار است. روش عددی، به طور کلی محاسبه پیچیده مسایل غیرخطی را اداره می کند. با این حال، دادن نقاط به یک منحنی و به دست آوردن منحنی کامل که اغلب پرهزینه و ...

Ergodicity of Stochastic Differential Equations Driven by Fractional Brownian Motion

We study the ergodic properties of finite-dimensional systems of SDEs driven by non-degenerate additive fractional Brownian motion with arbitrary Hurst parameter H ∈ (0, 1). A general framework is constructed to make precise the notions of “invariant measure” and “stationary state” for such a system. We then prove under rather weak dissipativity conditions that such an SDE possesses a unique st...

Stochastic Differential Equations Driven by a Fractional Brownian Motion

We study existence, uniqueness and regularity of some sto-chastic diierential equations driven by a fractional Brownian motion of any Hurst index H 2 (0; 1): 1. Introduction Fractional Brownian motion and other longgrange dependent processes are more and more studied because of their potential applications in several elds like telecommunications networks, nance markets, biology and so on The ma...

Stochastic Differential Equations Driven by Fractional Brownian Motion and Standard Brownian Motion

We prove an existence and uniqueness theorem for solutions of multidimensional, time dependent, stochastic differential equations driven simultaneously by a multidimensional fractional Brownian motion with Hurst parameter H > 1/2 and a multidimensional standard Brownian motion. The proof relies on some a priori estimates, which are obtained using the methods of fractional integration, and the c...

Flow properties of differential equations driven by fractional Brownian motion

We prove that solutions of stochastic differential equations driven by fractional Brownian motion for H > 1/2 define flows of homeomorphisms on R. AMS Subject Classification: 60H05, 60H07