Stochastic Processes with Memory. A volatility as a study case

      Аннотация: The aim of this book to derive stochastic model with memory effect. Short memory or Markovian model and long memory which is non-Markovian model. The methods are used called the conditional arrival probability and age model. The first can be used to derive model in a case of continuous time and discrete or continuous states. The second is used when the model has continuous time and discrete states. The waiting time distributions are the main factors that affect the memory of the models. In the case of long memory model, we get fractional time differential equation when the state space is discrete. However, we get fractional time-space differential equation when the state space is continuous.

Ключевые слова: Stochastic Model, Long Memory, short memory, Markovian property, non- markovian property