Stochastic differential equations and applications

Stochastic Differential Equations and Applications

The expressions of solutions for general n × m matrix-valued inhomogeneous linear stochastic differential equations are derived. This generalizes a result of Jaschke (2003) for scalar inhomogeneous linear stochastic differential equations. As an application, some IR vector-valued inhomogeneous nonlinear stochastic differential equations are reduced to random differential equations, facilitating...

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.

Stochastic Differential Equations with Applications

Conditioned Stochastic Differential Equations: Theory and Applications

We generalize the notion of brownian bridge. More precisely, we study a standard brownian motion for which a certain functional is conditioned to follow a given law. Such processes appear as weak solutions of stochastic differential equations which we call conditioned stochastic differential equations. The link with the theory of initial enlargement of filtration is made and after a general pre...

Backward Stochastic Differential Equations and Applications

A new type of stochastic differential equation, called the backward stochastic differentil equation (BSDE), where the value of the solution is prescribed at the final (rather than the initial) point of the time interval, but the solution is nevertheless required to be at each time a function of the past of the underlying Brownian motion, has been introduced recently, independently by Peng and t...