Linear operators generated by stochastic processes

M. Sh Braverman

doi:10.1007/BF01261270

Linear operators generated by stochastic processes

Research output: Contribution to journal › Article › peer-review

Abstract

Let X_t(0≤ t < ∞) be a homogeneous stochastically continuous stochastic process with independent increments; (Ω, A, P) be the corresponding probability space; p, q≥1 be fixed numbers. Necessary and sufficient conditions are found for a stochastic integral defined on finite-valued functions to be extendable to a bounded operator from L_p (0, ∞) to L_q(Ω) (p ≠ q).

Original language	English
Pages (from-to)	3156-3161
Number of pages	6
Journal	Journal of Soviet Mathematics
Volume	67
Issue number	4
DOIs	https://doi.org/10.1007/BF01261270
State	Published - 1 Jan 1993
Externally published	Yes

ASJC Scopus subject areas

Statistics and Probability
General Mathematics
Applied Mathematics

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10.1007/BF01261270

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title = "Linear operators generated by stochastic processes",

abstract = "Let Xt(0≤ t < ∞) be a homogeneous stochastically continuous stochastic process with independent increments; (Ω, A, P) be the corresponding probability space; p, q≥1 be fixed numbers. Necessary and sufficient conditions are found for a stochastic integral defined on finite-valued functions to be extendable to a bounded operator from Lp (0, ∞) to Lq(Ω) (p ≠ q).",

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N2 - Let Xt(0≤ t < ∞) be a homogeneous stochastically continuous stochastic process with independent increments; (Ω, A, P) be the corresponding probability space; p, q≥1 be fixed numbers. Necessary and sufficient conditions are found for a stochastic integral defined on finite-valued functions to be extendable to a bounded operator from Lp (0, ∞) to Lq(Ω) (p ≠ q).

AB - Let Xt(0≤ t < ∞) be a homogeneous stochastically continuous stochastic process with independent increments; (Ω, A, P) be the corresponding probability space; p, q≥1 be fixed numbers. Necessary and sufficient conditions are found for a stochastic integral defined on finite-valued functions to be extendable to a bounded operator from Lp (0, ∞) to Lq(Ω) (p ≠ q).

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Linear operators generated by stochastic processes

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