Iterative methods for approximate solution of the Ornstein- Uhlenbeck process with normalised brownian motion

This work considers the concept of the Normalised Brownian motion for the solutions of the Ornstein-Uhlenbeck process using the Daftardar-Jafari Method (DJM) and Picard Iterative Method (PIM) as the approximate-analytical methods of solutions. The results obtained from DJM are compared with those of the PIM. The obtained results, therefore, show the effectiveness of the proposed method

A computational method for solving stochastic ItÔ-Volterra integral equations based on stochastic operational matrix for generalized hat basis functions

In this paper, a new computational method based on the generalized hat basis functions is proposed for solving stochastic ItÔ-Volterra integral equations. In this way, a new stochastic operational matrix for generalized hat functions on the finite interval [0, T] is obtained. By using these basis functions and their stochastic operational matrix, such problems can be transformed into linear lower triangular systems of algebraic equations which can be directly solved by forward substitution. Also, the rate of convergence of the proposed method is considered and it has been shown that it is O(1n2). Further, in order to show the accuracy and reliability of the proposed method, the new approach is compared with the block pulse functions method by some examples. The obtained results reveal that the proposed method is more accurate and efficient in comparison with the block pule functions method. © 2014 Elsevier Inc

Notes in Pure Mathematics & Mathematical Structures in Physics

These Notes deal with various areas of mathematics, and seek reciprocal combinations, explore mutual relations, ranging from abstract objects to problems in physics.Comment: Small improvements and addition