Distribution dependent 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.

Stability in Distribution of Numerical Solutions for Stochastic Differential Equations

The numerical methods on stochastic differential equations (SDEs) have been well established. There are several papers that study the numerical stability of SDEs with respect to sample paths or moments. In this paper we study the stability in distribution of numerical solution of SDEs.

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

Stochastic Partial Differential Equations