Harmonizable fractional stable fields: Local nondeterminism and joint continuity of the local times
نویسندگان
چکیده
منابع مشابه
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...
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Let B = {B(t), t∈ RN+} be an (N,d)-fractional Brownian sheet with index H = (H1, . . . ,HN) ∈ (0,1) N defined by B(t) = (B 1 (t), . . . ,B H d (t)) (t∈ R N + ), where B H 1 , . . . ,B H d are independent copies of a real-valued fractional Brownian sheet B 0 . We prove that if d < ∑ N l=1 H l , then the local times of B are jointly continuous. This verifies a conjecture of Xiao and Zhang (Probab...
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We establish properties of strong local nondeterminism for several classes of α-stable random fields such as harmonizable-type fractional stable fields with stationary increments, harmonizable and linear fractional stable sheets. We apply these properties to study existence and joint continuity of the local times of stable random fields. Mathematics Subject Classification (2000). 60G52; 60G17; ...
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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...
Properties of local-nondeterminism of Gaussian and stable random fields and their applications
— In this survey, we first review various forms of local nondeterminism and sectorial local nondeterminism of Gaussian and stable random fields. Then we give sufficient conditions for Gaussian random fields with stationary increments to be strongly locally nondeterministic (SLND). Finally, we show some applications of SLND in studying sample path properties of (N, d)-Gaussian random fields. The...
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ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 2016
ISSN: 0304-4149
DOI: 10.1016/j.spa.2015.08.001