Preliminaries to Probability Theory and Stochastic Differential Equations

Vasile Dragan, Toader Morozan and Adrian-Mihail Stoica
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Vasile Dragan: Institute of Mathematics of the Romanian Academy
Toader Morozan: Institute of Mathematics of the Romanian Academy
Adrian-Mihail Stoica: University Politechnica of Bucharest

Chapter Chapter 1 in Mathematical Methods in Robust Control of Linear Stochastic Systems, 2013, pp 1-38 from Springer

Abstract: Abstract This first chapter collects for the readers convenience some definitions and fundamental results concerning the measure theory and the stochastic processes theory which are needed in the following developments of the book. Classical results concerning the measure theory, integration, stochastic processes, and stochastic integrals are presented without proofs. Appropriate references are given; thus for the measure theory we mention [33, 55, 71, 75, 118, 138]; for the probability theory we refer to [32, 71, 119, 130, 138], and for the theory of stochastic processes and stochastic differential equations we cite [6, 18, 32, 71, 72, 85, 102, 105, 120, 121, 141, 152, 153]. However several results which can be found in some references less accessible are proved.

Keywords: Random Vector; Stochastic Differential Equation; Conditional Expectation; Measure Theory; Stochastic Integral (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-8663-3_1

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DOI: 10.1007/978-1-4614-8663-3_1

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