A stochastic minimax optimal control strategy for uncertain quasi-Hamiltonian systems is proposed based on the stochastic averaging method, stochastic maximum principle and stochastic differential game theory. First, the partially completed averaged Itô stochastic differential equations are derived from a given system by using the stochastic averaging method for quasi-Hamiltonian systems with u...

in this paper, we present an efficient method for determining the solution of the stochastic second kind volterra integral equations (svie) by using the taylor expansion method. this method transforms the svie to a linear stochastic ordinary differential equation which needs specified boundary conditions. for determining boundary conditions, we use the integration technique. this technique give...

(Received ??) We describe a criterion for particles suspended in a randomly moving fluid to aggregate. Aggregation occurs when the expectation value of a random variable is negative. This variable evolves under a stochastic differential equation. We analyse this equation in detail in the limit where the correlation time of the velocity field of the fluid is very short, such that the stochastic ...

We introduce a new method of proving pathwise uniqueness, and we apply it to the degenerate stochastic differential equation dX t = |X t | α dW t , where W t is a one-dimensional Brownian motion and α ∈ (0, 1/2). Weak uniqueness does not hold for the solution to this equation. If one restricts attention, however, to those solutions that spend zero time at 0, then pathwise uniqueness does hold a...

In this paper, we present an efficient method for determining the solution of the stochastic second kind Volterra integral equations (SVIE) by using the Taylor expansion method. This method transforms the SVIE to a linear stochastic ordinary differential equation which needs specified boundary conditions. For determining boundary conditions, we use the integration technique. This technique give...

A generalised urn model is presented in this paper. The urn contains L different types of balls and its replacement policy depends on both an urn function and a random environment. We consider the Ldimensional stochastic process {Xn} that represents the proportion of balls of each type in the urn after each replacement. This process can be expressed as a stochastic recurrent equation that fits ...