We finished discussing Discrete-Time Markov Chains in the previous lecture, and are now heading towards Continuous-Time Markov Chains. Discrete-time Markov Chains are totally synchronized, whereas CTMCs are not. In preparation for CTMCs, we need to discuss the Exponential distribution and the Poisson arrival process. We say that a random variable X is distributed exponentially with rate λ, X ∼ ...

In this study we model the daily rainfall occurrence using Markov Chain Analogue Yearmodel (MCAYM) and the intensity or amount of daily rainfall using three different probability distributions; gamma, exponential and mixed exponential distributions. Combining the occurrence and intensity model we obtain Markov Chain Analogue Year gamma model (MCAYGM), Markov Chain Analogue Year exponentia...

In this paper we introduce an exponential continuous time GARCH(p, q) process. It is defined in such a way that it is a continuous time extension of the discrete time EGARCH(p, q) process. We investigate stationarity, mixing and moment properties of the new model. An instantaneous leverage effect can be shown for the exponential continuous time GARCH(p, p) model.

There has been increasing demand on psychodynamicially oriented therapists to empirically demonstrate the effectiveness of their interventions, and to associate these interventions with successful therapeutic outcome. Studies focused on psychoanalytic process have identified several process-related variables influencing the nature of the treatment and have demonstrated how therapy process chang...

We are used Bayes estimators for unknown scale parameter when shape Parameter is known of Erlang distribution. Assuming different informative priors parameter. derived The posterior density with mean and variance using which the inverse exponential distribution, chi-square Gamma standard Levy distribution as prior. And we based on general entropy loss function (GELF) Simulation method to obtain...

This study aims at getting a better performance for optimal stock portfolios by modeling stocks prices dynamics through a continuous paths Levy process. To this end, the share prices are simulated using a multi-dimensional geometric Brownian motion model. Then, we use the results to form the optimal portfolio by maximizing the Sharpe ratio and comparing the findings with the outputs of the conv...