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1969•The Annals of Mathematical StatisticsOpen access

Martingales with Independent Increments

P. Warwick Millar

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Abstract

In section one, $L_1$ bounds are obtained for transforms of discrete parameter martingales having independent increments. Section two develops the theory of quadratic variation for continuous parameter martingales having independent increments. An application of the results of these two sections to the theory of stochastic integrals appears in section three.

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In section one, $L_1$ bounds are obtained for transforms of discrete parameter martingales having independent increments. Section two develops the theory of quadratic variation for continuous parameter martingales having independent increments. An application of the results of these two sections to the theory of stochastic integrals appears in section three.

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Available abstract

In section one, $L_1$ bounds are obtained for transforms of discrete parameter martingales having independent increments. Section two develops the theory of quadratic variation for continuous parameter martingales having independent increments. An application of the results of these two sections to the theory of stochastic integrals appears in section three.

Key concepts: Mathematics, Quadratic variation, Section (typography), Quadratic equation, Mathematical analysis, Applied mathematics, Pure mathematics, Calculus (dental)

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