Large deviations for local time fractional Brownian motion and applications

Large deviations for local times and intersection local times of fractional Brownian motions and Riemann-Liouville processes

In this paper we prove exact forms of large deviations for local times and intersection local times of fractional Brownian motions and Riemann–Liouville processes. We also show that a fractional Brownian motion and the related Riemann–Liouville process behave like constant multiples of each other with regard to large deviations for their local and intersection local times. As a consequence of o...

Large deviations for the local and intersection local times of fractional Brownian motions

Large deviation principle for the non-linear functionals of non-Markovian models is a challenging subject. A class of such models are Gaussian processes. Among them, the fractional Brownian motions are perhaps the most important processes. In this talk, I will talk about some recent progress achieved in the large deviations for local times and intersection local times of fractional Brownian mot...

On time-dependent neutral stochastic evolution equations with a fractional Brownian motion and infinite delays

In this paper, we consider a class of time-dependent neutral stochastic evolution equations with the infinite delay and a fractional Brownian motion in a Hilbert space. We establish the existence and uniqueness of mild solutions for these equations under non-Lipschitz conditions with Lipschitz conditions being considered as a special case. An example is provided to illustrate the theory

A Variation Embedding Theorem and Applications

Fractional Sobolev spaces, also known as Besov or Slobodetzki spaces, arise in many areas of analysis, stochastic analysis in particular. We prove an embedding into certain q-variation spaces and discuss a few applications. First we show q-variation regularity of Cameron-Martin paths associated to fractional Brownian motion and other Volterra processes. This is useful, for instance, to establis...

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