Following is a quote from [3]. Stochastic differential equations provide a link between probability theory and the much older and more developed fields of ordinary and partial differential equations. Wonderful consequences flow in both directions. The stochastic modeler benefits from centuries of development of the physical sciences, and many classic results of mathematical physics (and even pu...

In this paper, we establish the existence of the solutions (X,L) of reflected stochastic differential equations with possible anticipating initial random variables. The key is to obtain some substitution formula for Stratonovich integrals via a uniform convergence of the corresponding Riemann sums.

We establish a large deviation principle for the solutions of stochastic partial differential equations for nonlinear vibration of elastic panels (also called stochastic nonlinear beam equations).

Stochastic partial differential equations are simply partial differential equations in the presence of uncertainty. Uncertainty, in its simplest form, is modeled by (or taken as) the time derivative (in the sense of distributions) of a Wiener process, known commonly as white noise. The introduction of a random force in a partial differential equation (PDE) arises from the need to explain the fl...

A highly nonnormal Jacobian may give rise to large transients. This behaviour has been shown to have implications for (a) the relevance of linearising a nonlinear system and (b) the timestep restrictions required to keep a numerical method stable. Here, we show that nonnormality also manifests itself for stochastic differential equations. We give an example of a family of systems that is stable...

A lot of discrete approximation schemes for stochastic differential equations with regard to mean-square sense were proposed. Numerical experiments for these schemes can be seen in some papers, but the efficiency of scheme with respect to its order has not been revealed. We will propose another type of error analysis. Also we will show results of simulation studies carried out for these schemes...

This homework has 200 points for MATP 6960 (260 points for MATP 4960) but, as always, homeworks are graded out of 100 points. Full credit will generally be awarded for a solution only if it is both correctly and efficiently presented using the techniques covered in the lecture and readings, and if the reasoning is properly explained. If you used software or simulations in solving a problem, be ...