Frequency domain methods for Volterra equations

Nohel, John A.; Shea, Daniel F.

doi:10.1016/0001-8708(76)90096-7

Cited by 145 publications

(51 citation statements)

References 16 publications

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“…A discussion of such kernels , and their implications concerning the stability of (V), appear in a large number of places , including MacCainy and Wong ( 4], and Nohel and Shea ( 5].…”

Section: Ductio Nmentioning

confidence: 99%

Positive Kernels and Stochastic Integrals

Berger¹

1979

SIAM J. Appl. Math.

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This report is intended to expand the applicability of positive kernel theory to probabilistic settings and stochastic integrals. The main result states that if a (t) is a positive kernel , and {8(t) : t > O} a Brownian motion , thenfor every stochastic process {~( t) : t > 0) which has a stochastic differential dE (t) with respect to 8 ( t) , and for every T > 0. The implication of (*) concerning energy estimates for certain Ito-Volterra equations is discussed , and examples are provided.

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“…A discussion of such kernels , and their implications concerning the stability of (V), appear in a large number of places , including MacCainy and Wong ( 4], and Nohel and Shea ( 5].…”

Section: Ductio Nmentioning

confidence: 99%

Positive Kernels and Stochastic Integrals

Berger¹

1979

SIAM J. Appl. Math.

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“…Let |a(f)| < M, 0 < f < T, \\f\\L«l0.T;H] < Mv and M2 be such that \x\ < 2MX implies |^°x| < M2. Then (3)(4)(5)(6)(7)(8)(9) \Ml-Io,,**] < 2Mv '6 = MX/MM2. Thus by an inequality similar to GronwalFs we have (3.12) \ux(t)-f(t)\<cf'\A0f(r)\dr.…”

Section: Jomentioning

confidence: 99%

Existence and Uniqueness of Solutions to Abstract Volterra Integral Equations

Kiffe¹,

Stecher²

1978

Proceedings of the American Mathematical Society

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“…An asymptotic problem. We continue as in [15] by studying the asymptotic problem: What does the condition (4.1) sup Re f <p*(t) [ dp(s)(p(t -s) dt) < oo The proof of Theorem 5.1 is the same as in the scalar case [11, §2] (line (2.4) in [11] becomes trivial because of (HI)).…”

Section: K-\jlot]mentioning

confidence: 99%