On the Distribution of the Integral of the Exponential Brownian Motion

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

A wavelet method for stochastic Volterra integral equations and its application to general stock model

In this article,we present a wavelet method for solving stochastic Volterra integral equations based on Haar wavelets. First, we approximate all functions involved in the problem by Haar Wavelets then, by substituting the obtained approximations in the problem, using the It^{o} integral formula and collocation points then, the main problem changes into a system of linear or nonlinear equation w...

Exponential functionals of Brownian motion, I: Probability laws at fixed time

This paper is the first part of our survey on various results about the distribution of exponential type Brownian functionals defined as an integral over time of geometric Brownian motion. Several related topics are also mentioned.

Three dimensional numerical study on a trapezoidal microchannel heat sink with different inlet/outlet arrangements utilizing variable properties nanofluid

Nowadays, microchannels as closed circuits channels for fluid flow and heat removal are an integral part of the silicon-based electronic microsystems. Most of previous numerical studies on microchannel heat sinks (MCHS) have been performed for a two-dimensional domain using constant properties of the working fluid. In this study, laminar fluid flow and heat transfer of variable properties Al2O3...

On Some Exponential Functionals of Brownian Motion

In this paper, distributional questions which arise in certain Mathematical Finance models are studied: the distribution of the integral over a fixed time interval {0, T} of the exponential of Brownian motion with drift is computed explicitly, with the help of former computations made by the author for Bessel processes. The moments of this integral are obtained independently and take a particul...

APPROXIMATION SOLUTION OF TWO-DIMENSIONAL LINEAR STOCHASTIC FREDHOLM INTEGRAL EQUATION BY APPLYING THE HAAR WAVELET

In this paper, we introduce an efficient method based on Haar wavelet to approximate a solutionfor the two-dimensional linear stochastic Fredholm integral equation. We also give an example to demonstrate the accuracy of the method.