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Random Linear Operators


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Table of Contents

1. Random Operators in Hilbert Space.- 1. Basic Definitions.- 2. Characteristic Functions of Random Operators.- 3. Convergence of Random Operators.- 2. Functions of Random Operators.- 4. Spectral Representation for Symmetric Random Operators.- 5. Equations with Symmetric Random Operators.- 6. Equations with Semi-Bounded Random Operators.- 3. Operator-Valued Martingales.- 7. Operator-Valued Martingale Sequences.- 8. Convergence of Infinite Products of Independent Random Operators.- 9. Continuous Operator-Valued Martingales.- 4. Stochastic Integrals and Equations.- 10. Stochastic Integrals with Respect to an X-Valued Martingale.- 11. Stochastic Integral with Respect to an Operator-Valued Martingale.- 12. Stochastic Operator Equations.- 5. Linear Stochastic Operator Equations.- 13. Generalization of the Stochastic Operator Integral.- 14. Linear Differential Operator Equations.- 15. Continuous Stochastic Semigroups.

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