Tempered fractional Brownian motion is obtained when the power law kernel in the moving average representation of a fractional Brownian motion is multiplied by an exponential tempering factor. This paper develops the theory of stochastic integrals for tempered fractional Brownian motion. Along the way, we develop some basic results on tempered fractional calculus.

We construct a martingale which has the same marginals as the arithmetic average of geometric Brownian motion. This provides a short proof of the recent result due to P. Carr et al [7] that the arithmetic average of geometric Brownian motion is increasing in the convex order. The Brownian sheet plays an essential role in the construction. Our method may also be applied when the Brownian motion ...

Several Brownian areas are considered in this paper: the Brownian excursion area, the Brownian bridge area, the Brownian motion area, the Brownian meander area, the Brownian double meander area, the positive part of Brownian bridge area, the positive part of Brownian motion area. We are interested in the asymptotics of the right tail of their density function. Inverting a double Laplace transfo...

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...

In this paper, stability theorems for stochastic differential equations and backward stochastic differential equations driven by G-Brownian motion are obtained. We show the existence and uniqueness of solutions to forward-backward stochastic differential equations driven by G-Brownian motion. Stability theorem for forward-backward stochastic differential equations driven by G-Brownian motion is...

Let X be a Brownian motion defined on the line (with X(0)=0) and let Y be an independent Brownian motion defined on the nonnegative real numbers. For all t ≥ 0, we define the iterated Brownian motion (IBM), Z, by setting Z t ∆ = X(Y t). In this paper we determine the exact uniform modulus of continuity of the process Z.

In this paper we investigate three discrete or semi-discrete approximation schemes for reflected Brownian motion on bounded Euclidean domains. For a class of bounded domains D in Rn that includes all bounded Lipschitz domains and the von Koch snowflake domain, we show that the laws of both discrete and continuous time simple random walks on D ∩ 2−kZn moving at the rate 2−2k with stationary init...

For the GI0GI01 queue we show that the scaled queue size converges to reflected Brownian motion in a critical queue and converges to reflected Brownian motion with drift for a sequence of subcritical queuing models that approach a critical model+ Instead of invoking the topological argument of the usual continuousmapping approach, we give a probabilistic argument using Skorokhod embeddings in B...

In this paper we investigate three discrete or semi-discrete approximation schemes for reflected Brownian motion on bounded Euclidean domains. For a class of bounded domains D in R that includes all bounded Lipschitz domains and the von Koch snowflake domain, we show that the laws of both discrete and continuous time simple random walks on D ∩ 2Z moving at the rate 2 with stationary initial dis...