Stationarity and stochastic differential equations

Stochastic differential equations and integrating factor

The aim of this paper is the analytical solutions the family of rst-order nonlinear stochastic differentialequations. We dene an integrating factor for the large class of special nonlinear stochasticdierential equations. With multiply both sides with the integrating factor, we introduce a deterministicdierential equation. The results showed the accuracy of the present work.

Simulating and Forecasting OPEC Oil Price Using Stochastic Differential Equations

The main purpose of this paper is to provide a quantitative analysis to investigate the behavior of the OPEC oil price. Obtaining the best mathematical equation to describe the price and volatility of oil has a great importance. Stochastic differential equations are one of the best models to determine the oil price, because they include the random factor which can apply the effect of different ...

Simulating Stochastic Differential Equations

Let S t be the time t price of a particular stock. We know that if S t ∼ GBM (µ, σ 2), then S t = S 0 e (µ−σ 2 /2)t+σBt (1) where B t is the Brownian motion driving the stock price. An alternative possibility is to use a stochastic differential equation (SDE) to describe the evolution of S t. In this case we would write S t = S 0 + t 0 µS u du + t 0 σS u dB u (2) or in shorthand , dS t = µS t d...

. Stochastic Differential Equations

Harmonic Analysis of Stochastic Equations and Backward Stochastic Differential Equations

The BMOmartingale theory is extensively used to study nonlinear multi-dimensional stochastic equations (SEs) inRp (p ∈ [1,∞)) and backward stochastic differential equations (BSDEs) in Rp × Hp (p ∈ (1,∞)) and in R∞ × H∞, with the coefficients being allowed to be unbounded. In particular, the probabilistic version of Fefferman’s inequality plays a crucial role in the development of our theory, wh...