Local Nondeterminism and Local Times of the Stochastic Wave Equation Driven by Fractional-Colored Noise

Stochastic Heat Equation Driven by Fractional Noise and Local Time

The aim of this paper is to study the d-dimensional stochastic heat equation with a multiplicative Gaussian noise which is white in space and it has the covariance of a fractional Brownian motion with Hurst parameter H ∈ (0, 1) in time. Two types of equations are considered. First we consider the equation in the Itô-Skorohod sense, and later in the Stratonovich sense. An explicit chaos developm...

Harmonizable Fractional Stable Fields: Local Nondeterminism and Joint Continuity of the Local Times

By applying a Fourier analytic argument, we prove that, for every α ∈ (0, 2), the N -parameter harmonizable fractional α-stable field (HFαSF) is locally nondeterministic. When 0 < α < 1, this solves an open problem in [15]. Also, it allows us to establish the joint continuity of the local times of an (N, d)-HFαSF for an arbitrary α ∈ (0, 2), and to obtain new results concerning its sample paths...

Stochastic Heat Equation with Multiplicative Fractional-Colored Noise

We consider the stochastic heat equation with multiplicative noise ut = 1 2 ∆u + uẆ in R+ × R , whose solution is interpreted in the mild sense. The noise Ẇ is fractional in time (with Hurst index H ≥ 1/2), and colored in space (with spatial covariance kernel f). When H > 1/2, the equation generalizes the Itô-sense equation for H = 1/2. We prove that if f is the Riesz kernel of order α, or the ...

ساختار کلاسهایی از حلقه های z- موضعی و c- موضعی the structure of some classes of z-local and c-local rings

فرض کنیمr یک حلقه تعویض پذیر ویکدار موضعی باشدو(j(r رایکال جیکوبسن r و(z(r مجموعه مقسوم علیه های صفر حلقه r باشد.گوییم r یک حلقه z- موضعی است هرگاه j(r)^2=. .همچنین برای یک حلقه تعویض پذیر r فرض کنیم c یک عنصر ناصفر از (z( r باشد با این خاصیت که cz( r)=0 گوییم حلقه موضعی r یک حلقه c - موضعی است هرگاه و{0 و z(r)^2={cو z(r)^3=0, نیز xz( r)=0 نتیجه دهد که x عضو {c,0 } است. در این پایان نامه ساخ...

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