Home Mathematics 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.5. Mean Square Stability of SDE Solutions. Stiff in Mean Square SDE Systems. Oscillatory Stochastic Systems
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2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.5. Mean Square Stability of SDE Solutions. Stiff in Mean Square SDE Systems. Oscillatory Stochastic Systems

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Numerical Analysis of Systems of Ordinary and Stochastic Differential Equations
This chapter is in the book Numerical Analysis of Systems of Ordinary and Stochastic Differential Equations

Chapters in this book

  1. I-VIII I
  2. 1. Numerical Solution of the Cauchy Problem for Systems of Ordinary Differential Equations 1
  3. 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations 49
  4. 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.1. Elements of Probability Theory, Stochastic Processes and Statistical Simulation 50
  5. 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.2. Cauchy Problem for a SDE System. Main Definitions 57
  6. 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.3. Construction of SDEs with Given Probability Characteristics of Solution 64
  7. 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.4. Linear SDE Systems with Additive and Multiplicative Noise 73
  8. 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.5. Mean Square Stability of SDE Solutions. Stiff in Mean Square SDE Systems. Oscillatory Stochastic Systems 79
  9. 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.6. Simple Numerical Methods Generalizing the Explicit Runge-Kutta Methods 85
  10. 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.7. Families of Numerical Methods for Solving SDE Systems. Theorem of Convergence 90
  11. 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.8. Mean Square Consistency of Methods 94
  12. 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.9. Mean Square Stability of Methods 106
  13. 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.10. Numerical Methods for Solving Linear SDE Systems 116
  14. 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.11. Variable Step Algorithms for Solving SDEs 120
  15. 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.12. Numerical Solution of SDE System with Poisson Component 128
  16. 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.13. Applying SDE for Numerical Solution of Linear Elliptic and Parabolic Equations 133
  17. 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.14. Statistical Simulation of the SDE Solutions in Problems of Analysis and Synthesis of Automated Control 139
  18. 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.15. Numerical Experiments 154
  19. References 169
https://doi.org/10.1515/9783110944662.79

Chapters in this book

  1. I-VIII I
  2. 1. Numerical Solution of the Cauchy Problem for Systems of Ordinary Differential Equations 1
  3. 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations 49
  4. 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.1. Elements of Probability Theory, Stochastic Processes and Statistical Simulation 50
  5. 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.2. Cauchy Problem for a SDE System. Main Definitions 57
  6. 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.3. Construction of SDEs with Given Probability Characteristics of Solution 64
  7. 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.4. Linear SDE Systems with Additive and Multiplicative Noise 73
  8. 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.5. Mean Square Stability of SDE Solutions. Stiff in Mean Square SDE Systems. Oscillatory Stochastic Systems 79
  9. 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.6. Simple Numerical Methods Generalizing the Explicit Runge-Kutta Methods 85
  10. 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.7. Families of Numerical Methods for Solving SDE Systems. Theorem of Convergence 90
  11. 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.8. Mean Square Consistency of Methods 94
  12. 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.9. Mean Square Stability of Methods 106
  13. 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.10. Numerical Methods for Solving Linear SDE Systems 116
  14. 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.11. Variable Step Algorithms for Solving SDEs 120
  15. 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.12. Numerical Solution of SDE System with Poisson Component 128
  16. 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.13. Applying SDE for Numerical Solution of Linear Elliptic and Parabolic Equations 133
  17. 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.14. Statistical Simulation of the SDE Solutions in Problems of Analysis and Synthesis of Automated Control 139
  18. 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.15. Numerical Experiments 154
  19. References 169
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