We present a formal theorem of the square root of the Brownian motion. In doing so, we show that this process can be presented as a typical complex random variable. In addition, we introduce the basic properties of this process

We study the correct estimation of the true variance of the predictor in stochastic Kriging (SK). First, we obtain macroreplications for a SK metamodel that approximates a single-server simulation model; these macroreplications give independently and identically distributed predictions. This...

Leshno and Levy (2002) introduce the concept of the first and second order of almost stochastic dominance (ASD) for most decision makers. There are many studies investigating the properties of this concept. Many empirical applications are also conducted based on it. However, there is no formal...

This paper introduces a new modelling framework for energy spot prices based on Lévy semistationary processes. Lévy semistationary processes are special cases of the general class of ambit processes. We provide a detailed analysis of the probabilistic properties of such models and we show how...

Ambit processes are general stochastic processes based on stochastic integrals with respect to Lévy bases. Due to their flexible structure, they have great potential for providing realistic models for various applications such as in turbulence and finance. This papers studies the connection...

We propose novel nonparametric estimators for stochastic volatility and the volatility of volatility. In doing so, we relax the assumption of a constant volatility of volatility and therefore, we allow the volatility of volatility to vary over time. Our methods are exceedingly simple and far...

Large-dimensional dynamic factor models and dynamic stochastic general equilibrium models, both widely used in empirical macroeconomics, deal with singular stochastic vectors, i.e., vectors of dimension r which are driven by a q-dimensional white noise, with q r. The present paper studies...

Both stochastic dominance and Omegaratio can be used to examine whether the market is efficient, whether there is any arbitrage opportunity in the market and whether there is any anomaly in the market. In this paper, we first study the relationship between stochastic dominance and the Omega...

Kriging provides metamodels for deterministic and random simulation models. Actually, there are several types of Kriging; the classic type is so-called universal Kriging, which includes ordinary Kriging. These classic types require estimation of the trend in the input-output data of the...

This paper is on decision theoretical foundations for various types of VaR models, including VaR and conditional-VaR, as objective measures of downside risk for financial prospects. We establish the connections of the VaRs with the first- and the second-order stochastic dominance investment...