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The Inequality of Nonlinear Conditional Expectations and Laws of Large Numbers

Yufeng Qiu

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Abstract

In this paper, the concepts of conditional expectation and conditional variance on the global NPC space are introduced. We investigate the inequalities of nonlinear conditional expectation and variance. Moreover, we prove the convergence in L2 and strong laws of large numbers for sequence of i.i.d. random variables with values in a metric space, the Jensen’s inequality for conditional expectation is finally derived.

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What this paper is about

In this paper, the concepts of conditional expectation and conditional variance on the global NPC space are introduced. We investigate the inequalities of nonlinear conditional expectation and variance. Moreover, we prove the convergence in L2 and strong laws of large numbers for sequence of i.i.d. random variables with values in a metric space, the Jensen’s inequality for conditional expectation is finally derived.

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Available abstract

In this paper, the concepts of conditional expectation and conditional variance on the global NPC space are introduced. We investigate the inequalities of nonlinear conditional expectation and variance. Moreover, we prove the convergence in L2 and strong laws of large numbers for sequence of i.i.d. random variables with values in a metric space, the Jensen’s inequality for conditional expectation is finally derived.

Key concepts: Mathematics, Conditional variance, Conditional expectation, Variance (accounting), Regular conditional probability, Nonlinear system, Conditional probability distribution, Sequence (biology)

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