In 2005, Nualart and Peccati [12] showed the so-called Fourth Moment Theorem asserting that, for a sequence of normalized multiple Wiener-Itô integrals to converge to the standard Gaussian law, it is necessary and sufficient that its fourth moment tends to 3. A few years later, Kemp et al. [8] extended this theorem to a sequence of normalized multiple Wigner integrals, in the context of the fre...

A theorem characterizing fractional Brownian motion by Index Terms -Wavelet transform, fractional Brownian motion.the covariance structure of its wavelet transform is established.

Purposeful motion of biological processes can be driven by Brownian motion of macromolecular complexes with one-sided binding biasing movement in one direction: a Brownian ratchet, now proposed to explain membrane motion during a phagocytosis-like process in bacteria.

We describe the CGMY and Meixner processes as time changed Brownian motions. The CGMY uses a time change absolutely continuous with respect to the one-sided stable (Y/2) subordinator while the Meixner time change is absolutely continuous with respect to the one sided stable (1/2) subordinator. The required time changes may be generated by simulating the requisite one-sided stable subordinator a...

We will introduce a class of (m-times) integrated Brownian motions. The exact asymptotic expansions for the L2 small ball probabilities will be discussed for members of this class, of which the usual m-times integrated Brownian motion is an example. Another example will be what we call an Euler-integrated Brownian motion. We will also find very sharp estimates for the asymptotics of the eigenva...

Abstract Using the framework of random walks in random scenery, Cohen and Samorodnitsky (2006) introduced a family of symmetric α-stable motions called local time fractional stable motions. When α = 2, these processes are precisely fractional Brownian motions with 1/2 < H < 1. Motivated by random walks in alternating scenery, we find a complementary family of symmetric α-stable motions which we...

In this paper an arbitrage strategy is constructed for the modified Black-Scholes model driven by fractional Brownian motion or by a time changed fractional Brownian motion, when the volatility is stochastic. This latter property allows the heavy tailedness of the log returns of the stock prices to be also accounted for in addition to the long range dependence introduced by the fractional Brown...

It has been demonstrated that Brownian models are effective for approximate analysis of queueing networks, particularly when no explicit analytical methods are available [3,4,1]. In 1988 Harrison [2] proposed Brownian models as approximations for multiclass open queueing networks. That work was expanded by Harrison and Nguyen in two recent papers [3,4] with the aim of developing a systematic me...

We define weighted fractional Brownian sheets, which are a class of Gaussian random fields with four parameters that include fractional Brownian sheets as special cases, and we give some of their properties. We show that for certain values of the parameters the weighted fractional Brownian sheets are obtained as limits in law of occupation time fluctuations of a stochastic particle model. In co...

We use recent results on the Fourier analysis of the zero sets of Brownian motion to explore the diophantine properties of an algorithmically random Brownian motion ( also known as a complex oscillation). We discuss the construction and definability of perfect sets which are linearly independent over the rationals directly from Martin-Löf random reals. Finally we explore the recent work of Tsir...