• Title/Summary/Keyword: Q-Wiener process

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BOUNDARY-VALUED CONDITIONAL YEH-WIENER INTEGRALS AND A KAC-FEYNMAN WIENER INTEGRAL EQUATION

  • Park, Chull;David Skoug
    • Journal of the Korean Mathematical Society
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    • v.33 no.4
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    • pp.763-775
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    • 1996
  • For $Q = [0,S] \times [0,T]$ let C(Q) denote Yeh-Wiener space, i.e., the space of all real-valued continuous functions x(s,t) on Q such that x(0,t) = x(s,0) = 0 for every (s,t) in Q. Yeh [10] defined a Gaussian measure $m_y$ on C(Q) (later modified in [13]) such that as a stochastic process ${x(s,t), (s,t) \epsilon Q}$ has mean $E[x(s,t)] = \smallint_{C(Q)} x(s,t)m_y(dx) = 0$ and covariance $E[x(s,t)x(u,\upsilon)] = min{s,u} min{t,\upsilon}$. Let $C_\omega \equiv C[0,T]$ denote the standard Wiener space on [0,T] with Wiener measure $m_\omega$. Yeh [12] introduced the concept of the conditional Wiener integral of F given X, E(F$\mid$X), and for case X(x) = x(T) obtained some very useful results including a Kac-Feynman integral equation.

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Optimal Design of Accelerated Degradation Tests under the Constraint of Total Experimental Cost in the Case that the Degradation Characteristic Follows a Wiener Process (열화가 Wiener process를 따르는 경우의 비용을 고려한 가속열화시험 계획)

  • Lim, Heon-Sang
    • Journal of Korean Society for Quality Management
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    • v.40 no.2
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    • pp.117-125
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    • 2012
  • For the highly reliable products, an accelerated degradation test (ADT) is a useful tool which has been employed in industry to obtain reliability-related information within an affordable amount of time and cost. In an ADT, as all other reliability tests, it is important to carefully design the ADT beforehand to obtain estimates of the quantities of interest as precisely as possible. In this paper, optimal ADTs are developed assuming that the constant-stress loading method is employed and the degradation characteristic follows a Wiener process. Under the constraint that the total cost does not exceed a pre-specified budget, the stress levels, the number of test units allocated to each stress level and the number of measurement (termination time) are determined such that the asymptotic variance of the maximum likelihood estimator of the q-th quantile of the lifetime distribution at the use condition is minimized.

BOUNDEDNESS AND CONTINUITY OF SOLUTIONS FOR STOCHASTIC DIFFERENTIAL INCLUSIONS ON INFINITE DIMENSIONAL SPACE

  • Yun, Yong-Sik;Ryu, Sang-Uk
    • Bulletin of the Korean Mathematical Society
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    • v.44 no.4
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    • pp.807-816
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    • 2007
  • For the stochastic differential inclusion on infinite dimensional space of the form $dX_t{\in}\sigma(X_t)dW_t+b(X_t)dt$, where ${\sigma}$, b are set-valued maps, W is an infinite dimensional Hilbert space valued Q-Wiener process, we prove the boundedness and continuity of solutions under the assumption that ${\sigma}$ and b are closed convex set-valued satisfying the Lipschitz property using approximation.

STOCHASTIC INTEGRAL OF PROCESSES TAKING VALUES OF GENERALIZED OPERATORS

  • CHOI, BYOUNG JIN;CHOI, JIN PIL;JI, UN CIG
    • Journal of applied mathematics & informatics
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    • v.34 no.1_2
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    • pp.167-178
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    • 2016
  • In this paper, we study the stochastic integral of processes taking values of generalized operators based on a triple E ⊂ H ⊂ E, where H is a Hilbert space, E is a countable Hilbert space and E is the strong dual space of E. For our purpose, we study E-valued Wiener processes and then introduce the stochastic integral of L(E, F)-valued process with respect to an E-valued Wiener process, where F is the strong dual space of another countable Hilbert space F.