This paper suggests a perfect-information game, along the lines of Lévy’s characterization of Brownian motion, that formalizes the process of Brownian motion in game-theoretic probability. This is perhaps the simplest situation where probability emerges in a non-stochastic environment.

Let B be a Brownian motion. We show that there is a process H predictable in the natural filtration of B, such that H ·S is a Brownian motion in its own filtration, where St =Bt+t. In other words, H hides the constant drift. This gives a positive answer to a question posed by Marc Yor.

The traffic patterns of today’s IP networks exhibit two important properties: self-similarity and long-range dependence. The fractional Brownian motion is widely used for representing the traffic model with the properties. We consider a single server fluid queueing system with input process of a fractional Brownian motion type. Formulas for effective bandwidth are derived in a single source and...

We consider a problem of an optimal consumption strategy on the infinite time horizon when the short-rate is a diffusion process. General existence and uniqueness theorem is illustrated by the Vasicek and so-called invariant interval models. We show also that when the short-rate dynamics is given by a Brownian motion or a geometric Brownian motion, then the value function is infinite.

Brownian-Laplace motion is a Lévy process which has both continuous (Brownian) and discontinuous (Laplace motion) components. The increments of the process follow a generalized normal Laplace (GNL) distribution which exhibits positive kurtosis and can be either symmetrical or exhibit skewness. The degree of kurtosis in the increments increases as the time between observations decreases. This an...

We review all recent contributions to the literature on stochastic processes. In particular, the Relativistic OrnsteinUhlenbeck Process is presented in detail, as is the intrinsic Brownian motion studied by Franchi and Le Jan. The Relativistic Brownian Motion of Dunkel and Hänggi is also reviewed, together with a model introduced by Oron and Horwitz. We finally suggest some possible future deve...

In this paper, we provide a scheme for simulating one-dimensional processes generated by divergence or non-divergence form operators with discontinuous coe cients. We use a space bijection to transform such a process in another one that behaves locally like a Skew Brownian motion. Indeed the behavior of the Skew Brownian motion can easily be approached by an asymmetric random walk.

The small ball problem for the integrated process of a real{valued Brownian motion is solved. In sharp contrast to more standard methods, our approach relies on the sample path properties of Brownian motion together with facts about local times and L evy processes.

An important determinant of option prices is the elasticity of the pricing kernel used to price all claims in the economy. In this paper, we rst show that for a given forward price of the underlying asset, option prices are higher when the elasticity of the pricing kernel is declining than when it is constant. We then investigate the implications of the elasticity of the pricing kernel for the ...

An important determinant of option prices is the elasticity of the pricing kernel used to price all claims in the economy. In this paper, we first show that for a given forward price of the underlying asset, option prices are higher when the elasticity of the pricing kernel is declining than when it is constant. We then investigate the implications of the elasticity of the pricing kernel for th...