Related papers: Local times for multifractional square Gaussian pr…

The stochastic calculus for Gaussian processes is applied to obtain a Tanaka formula for a Volterra-type multifractional Gaussian process. The existence and regularity properties of the local time of this process are obtained by means of…

Let $Z = (Z_t)_{t \geq 0}$ be the Rosenblatt process with Hurst index $H \in (1/2, 1)$. We prove joint continuity for the local time of $Z$, and establish H\"older conditions for the local time. These results are then used to study the…

We study the existence and regularity of local times for general $d$-dimensional stochastic processes. We give a general condition for their existence and regularity properties. To emphasize the contribution of our results, we show that…

We provide a sufficient condition for the continuity of real valued permanental processes. When applied to the subclass of permanental processes which consists of squares of Gaussian processes, we obtain the sufficient condition for…

The aim of this work is to define and perform a study of local times of all Gaussian processes that have an integral representation over a real interval (that maybe infinite). Very rich, this class of Gaussian processes, contains Volterra…

Ito's Lemma implies that if $W$ is a Wiener process and $f$ is a twice continuously differentiable function, then the process $f(W)$ is the sum of a time integral and an Ito integral. The Ito integrand is not necessarily locally square…

Generalised Ito formulae are proved for time dependent functions of continuous real valued semi-martingales. The conditions involve left space and time first derivatives, with the left space derivative required to have locally bounded…

In present paper we prove an existence and give a moments estimate for the local time of Gaussian integrators. Every Gaussian integrator is associated with a continuous linear operator in the space of square integrable functions via white…

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…

In this article we discuss the existence of local time for a class of Gaussian processes which appears as the solutions to some stochastic evolution equations. We show that on small intervals such processes are Gaussian integrators…

In this article, we consider fractional derivatives of local time for $d-$dimensional centered Gaussian processes satisfying certain strong local nondeterminism property. We first give a condition for existence of fractional derivatives of…

We study a Volterra Gaussian process of the form $X(t)=\int^t_0K(t,s)d{W(s)},$ where $W$ is a Wiener process and $K$ is a continuous kernel. In dimension one, we prove a law of the iterated logarithm, discuss the existence of local times…

In present article we prove the existence of multiple self-intersection local times, describe its Ito-Wiener expansion and establish Clark representation for the class of Gaussian integrators generated by operators with a finite dimensional…

This paper provides an existence-and-uniqueness theorem characterizing the stochastic integral with respect to a Wiener process. The integral is represented as a mapping from the space of measurable and adapted pathwise locally integrable…

In this paper we establish the existence of a square integrable occupation density for two classes of stochastic processes. First we consider a Gaussian process with an absolutely continuous random drift, and secondly we handle the case of…

We show that the derivative of the intersection and self-intersection local times of alpha-stable processes are exponentially integrable for certain parameter values. This includes the Brownian motion case. We also discuss related results…

We establish estimates for the local and uniform moduli of continuity of the local time of multifractional Brownian motion, $B^H=(B^{H(t)}(t),t\in\mathbb{R}^+)$. An analogue of Chung's law of the iterated logarithm is studied for $B^H$ and…

We present a general method for constructing stochastic processes with prescribed local form. Such processes include variable amplitude multifractional Brownian motion, multifractional $\alpha$-stable processes, and multistable processes,…

We show an It\^ o's formula for nondegenerate Brownian martingales $X_t=\int_0^t u_s dW_s$ and functions $F(x,t)$ with locally integrable derivatives in $t$ and $x$. We prove that one can express the additional term in It\^o's s formula as…

In this paper, we combine Hida distribution theory and Sobolev-Watanabe-Kree spaces in order to study finely the link between forward integrals obtained by regularization and Wick-It\^o integrals with respect to fractional Brownian motion…