Related papers: Holder continuity and occupation-time formulas for…

We give the correct condition for existence of the $k$-th derivative of the intersection local time for fractional Brownian motion, which was originally discussed in [Guo, J., Hu, Y., and Xiao, Y., Higher-order derivative of intersection…

We consider the existence and H\"{o}lder continuity conditions for the $k$-th order derivatives of self-intersection local time for $d$-dimensional fractional Brownian motion, where $k=(k_1,k_2,\cdots, k_d)$. Moreover, we show a limit…

We prove a conditional local limit theorem for discrete-time fractional Brownian motions (dfBm) with Hurst parameter 3/4<H<1. Using results from infinite ergodic theory it is then shown that the properly scaled occupation time of dfBm…

We prove the existence of the intersection local time for two independent, d -dimensional fractional Brownian motions with the same Hurst parameter H. Assume d greater or equal to 2, then the intersection local time exists if and only if…

The existence condition $H<1/d$ for first-order derivative of self-intersection local time for $d\geq3$ dimensional fractional Brownian motion can be obtained in Yu (2021). In this paper, we show a limit theorem under the non-existence…

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…

In this paper, we study the existence and (H\"older) regularity of local times of stochastic differential equations driven by fractional Brownian motions. In particular, we show that in one dimension and in the rough case H<1/2, the…

The derivative of self-intersection local time (DSLT) for Brownian motion was introduced by Rosen and subsequently used by others to study the $L^2$ and $L^3$ moduli of continuity of Brownian local time. A version of the DSLT for fractional…

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 give a result of stability in law of the local time of the fractional Brownian motion with respect to small perturbations of the Hurst parameter. Concretely, we prove that the law (in the space of continuous functions) of the local time…

We investigate first and second order fluctuations of additive functionals of a fractional Brownian motion (fBm) of the form \begin{align}\label{eq:abstractmain} Z_n=\left\{\int_{0}^{t}f(n^{H}(B_{s}-\lambda))ds\ ; t\geq 0 \right\}…

Let $\{B_{t}\}_{t\geq0}$ be a $d$-dimensional fractional Brownian motion with Hurst parameter $0<H<1$, where $d\geq2$. Consider the approximation of the self-intersection local time of $B$, defined as \begin{align*} I_{T}^{\varepsilon}…

Let $\{B_{t}\}_{t\geq0}$ be a fractional Brownian motion with Hurst parameter $\frac{2}{3}<H<1$. We prove that the approximation of the derivative of self-intersection local time, defined as \begin{align*} \alpha_{\varepsilon} &=…

In this article, we obtain sharp conditions for the existence of the high order derivatives ($k$-th order) of intersection local time $ \widehat{\alpha}^{(k)}(0)$ of two independent d-dimensional fractional Brownian motions $B^{H_1}_t$ and…

For $0<\alpha \leq 2$ and $0<H<1$, an $\alpha$-time fractional Brownian motion is an iterated process $Z = \{Z(t)=W(Y(t)), t \ge 0\}$ obtained by taking a fractional Brownian motion $\{W(t), t\in \RR{R} \}$ with Hurst index $0<H<1$ and…

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…

We consider the occupation area of spherical (fractional) Brownian motion, i.e. the area where the process is positive, and show that it is uniformly distributed. For the proof, we introduce a new simple combinatorial view on occupation…

We consider various problems related to the persistence probability of fractional Brownian motion (FBM), which is the probability that the FBM $X$ stays below a certain level until time $T$. Recently, Oshanin et al. study a physical model…

Sticky Brownian motion on the real line can be obtained as a weak solution of a system of stochastic differential equations. We find the conditional distribution of the process given the driving Brownian motion, both at an independent…

Denote by $H(t)=(H_1(t),...,H_N(t))$ a function in $t\in{\mathbb{R}}_+^N$ with values in $(0,1)^N$. Let $\{B^{H(t)}(t)\}=\{B^{H(t)}(t),t\in{\mathbb{R}}^N_+\}$ be an $(N,d)$-multifractional Brownian sheet (mfBs) with Hurst functional $H(t)$.…