Related papers: Perpetual Integral Functionals of Multidimensional…
The definition of infinite dimensional Fresnel integrals is generalized to the case of polynomial phase functions of any degree and applied to the construction of a functional integral representation of the solution of a general class of…
We give a new estimate on Stieltjes integrals of H\"older continuous functions and use it to prove an existence-uniqueness theorem for solutions of ordinary differential equations with H\"older continuous forcing. We construct stochastic…
We provide explicit series expansions to certain stochastic path-dependent integral equations in terms of the path signature of the time augmented driving Brownian motion. Our framework encompasses a large class of stochastic linear…
Let ${\mathscr L}^H(x,t)=2H\int_0^t\delta(B^H_s-x)s^{2H-1}ds$ be the weighted local time of fractional Brownian motion $B^H$ with Hurst index $1/2<H<1$. In this paper, we use Young integration to study the integral of determinate functions…
We construct a stochastic process whose drift is a function of the process's local time at a reflecting barrier. The process arose as a model of the interactions of a Brownian particle and an inert particle in (Knight, 2001). Interesting…
In the article random functions in modules over the octonion algebra and Cayley-Dickson algebras are investigated. For their study transition measures with values in the octonion algebra and Cayley-Dickson algebras are used. Stochastic…
Fractional renewal processes as a generalization of Poisson process are already in the literature. In this paper, by introducing a new concept of generalized density function, the authors construct new fractional renewal processes in the…
Consider an n-fold integrated Brownian motion. We show that a simple change in time and scale transforms it into a stationary Gaussian process. The collection of stationary processes so constructed not only constitutes an interesting family…
Introduced is the notion of minimality for spectral representations of sum- and max-infinitely divisible processes and it is shown that the minimal spectral representation on a Borel space exists and is unique. This fact is used to show…
This paper aims to evaluate the Piterbarg-Berman function given by $$\mathcal{P\!B}_\alpha^h(x, E) = \int_\mathbb{R}e^z\mathbb{P} \left\{{\int_E \mathbb{I}\left(\sqrt2B_\alpha(t) - |t|^\alpha - h(t) - z>0 \right) {\text{d}} t > x} \right\}…
A set of exact integrals of motion is found for systems driven by homogenous isotropic stochastic flow. The integrals of motion describe the evolution of (hyper-)surfaces of different dimensions transported by the flow, and can be expressed…
We consider the Markov random flight $\bold X(t)$ in the Euclidean space $\Bbb R^m, \; m\ge 2,$ starting from the origin $\bold 0\in\Bbb R^m$ that, at Poisson-paced times, changes its direction at random according to arbitrary distribution…
We investigate a Verhulst process, which is the special functional of geometric Brownian motion and has many applications, among others in biology and in stochastic volatility models. We present an exact form of density of a one dimensional…
The focus of this article is on entropy and Markov processes. We study the properties of functionals which are invariant with respect to monotonic transformations and analyze two invariant "additivity" properties: (i) existence of a…
We achieve the multifractal analysis of a class of complex valued statistically self-similar continuous functions. For we use multifractal formalisms associated with pointwise oscillation exponents of all orders. Our study exhibits new…
We show that every separable Gaussian process with integrable variance function admits a Fredholm representation with respect to a Brownian motion. We extend the Fredholm representation to a transfer principle and develop stochastic…
In this paper, we investigate the stationarity of stochastic processes in the fractional Fourier domains. We study the stationarity of a stochastic process after performing fractional Fourier transform (FRFT), and discrete fractional…
Our aim in this article is to provide explicit computable estimates for the cumulative distribution function (c.d.f.) and the $p$-th order moment of the exponential functional of a fractional Brownian motion (fBM) with drift. Using…
Let $X=(X_t)_{t\geq 0}$ be a one-dimensional L\'evy process such that each $X_t$ has a $C^1_b$-density w.r.t. Lebesgue measure and certain polynomial or exponential moments. We characterize all polynomially bounded functions…
The paper is devoted to the properties of the entropy of the exponent-Wiener-integral fractional Gaussian process (EWIFG-process), that is a Wiener integral of the exponent with respect to fractional Brownian motion. Unlike fractional…