Limit Theorems for Stochastic Processes

1. Front Matter

   Pages I-XVII

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2. The General Theory of Stochastic Processes, Semimartingales and Stochastic Integrals

   • Jean Jacod, Albert N. Shiryaev

   Pages 1-63

3. Characteristics of Semimartingales and Processes with Independent Increments

   • Jean Jacod, Albert N. Shiryaev

   Pages 64-128

4. Martingale Problems and Changes of Measures

   • Jean Jacod, Albert N. Shiryaev

   Pages 129-190

5. Hellinger Processes, Absolute Continuity and Singularity of Measures

   • Jean Jacod, Albert N. Shiryaev

   Pages 191-247

6. Contiguity, Entire Separation, Convergence in Variation

   • Jean Jacod, Albert N. Shiryaev

   Pages 248-287

7. Skorokhod Topology and Convergence of Processes

   • Jean Jacod, Albert N. Shiryaev

   Pages 288-347

8. Convergence of Processes with Independent Increments

   • Jean Jacod, Albert N. Shiryaev

   Pages 348-414

9. Convergence to a Process with Independent Increments

   • Jean Jacod, Albert N. Shiryaev

   Pages 415-479

10. Convergence to a Semimartingale

    • Jean Jacod, Albert N. Shiryaev

    Pages 480-534

11. Limit Theorems, Density Processes and Contiguity

    • Jean Jacod, Albert N. Shiryaev

    Pages 535-571

12. Back Matter

    Pages 572-604

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Initially the theory of convergence in law of stochastic processes was developed quite independently from the theory of martingales, semimartingales and stochastic integrals. Apart from a few exceptions essentially concerning diffusion processes, it is only recently that the relation between the two theories has been thoroughly studied. The authors of this Grundlehren volume, two of the international leaders in the field, propose a systematic exposition of convergence in law for stochastic processes, from the point of view of semimartingale theory, with emphasis on results that are useful for mathematical theory and mathematical statistics. This leads them to develop in detail some particularly useful parts of the general theory of stochastic processes, such as martingale problems, and absolute continuity or contiguity results. The book contains an elementary introduction to the main topics: theory of martingales and stochastic integrales, Skorokhod topology, etc., as well as a large number of results which have never appeared in book form, and some entirely new results. It should be useful to the professional probabilist or mathematical statistician, and of interest also to graduate students.

• Martingal
• Martingale
• Semimartingal
• Semimartingale
• Variation
• diffusion process
• statistics
• stochastic processes

• Laboratoire de Probabilités, Paris 05, France

  Jean Jacod

• Steklov Mathematical Institute, Moscow, USSR

  Albert N. Shiryaev

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