Related papers: A Counterexample in Ito Integration Theory

We study the convergence to the multiple Wiener-It\^{o} integral from processes with absolutely continuous paths. More precisely, consider a family of processes, with paths in the Cameron-Martin space, that converges weakly to a standard…

Lindel{\"o}f's hypothesis, one of the most important open problems in the history of mathematics, states that for large $t$, Riemann's zeta function $\zeta(1/2+it)$ is of order $O(t^{\varepsilon})$ for any $\varepsilon>0$ . It is well known…

We consider integrals $\tau_{\rho}=\int_0^1\rho\xi^2\,dx$, where $\xi$ is Wiener process and $\rho$ is generalized function from some class of multipliers. In the case when multiplier $\rho$ belongs to the trace-class, it is shown that…

We show that for every ergodic and aperiodic probability preserving system, there exists a $\mathbb{Z}$ valued, square integrable function $f$ such that the partial sums process of the time series $\left\{f\circ T^i\right\}_{i=0}^\infty$…

For a sequence of complex Wiener-Ito multiple integrals, the equivalence between the convergence of the symmetrized contraction norms and that of the non-symmetrized contraction norms is shown directly by means of a new version of complex…

Symmetries can be used to integrate scalar Ito equation -- or reduce systems of such equations -- by the Kozlov substitution, i.e. passing to symmetry adapted coordinates. While the theory is well established for so called deterministic…

Using the theory of stochastic integration for processes with values in a UMD Banach space developed recently by the authors, an Ito formula is proved which is applied to prove the existence of strong solutions for a class of stochastic…

Let a function f with real poles be expanded in a Wolff-Denjoy series with positive coefficients. The main result of the note states that if we subtract its linear part from the function 1/f, then the remaining fractional part of this…

Hermite processes are a class of self-similar processes with stationary increments. They often arise in limit theorems under long-range dependence. We derive new representations of Hermite processes with multiple Wiener-It\^o integrals,…

In this note we shall study the Witten multiple zeta function associated to the Lie algebra so(5) defined by Matsumoto. Our main result shows that its special values at nonnegative integers are always expressible by alternating Euler sums.…

This paper gives several simple constructions of the pathwise Ito integral $\int_0^t\phi d\omega$ for an integrand $\phi$ and a price path $\omega$ as integrator, with $\phi$ and $\omega$ satisfying various topological and analytical…

Bardina and Jolis [Stochastic process. Appl. 69 (1997) 83--109] prove an extension of It\^{o}'s formula for $F(X_t,t)$, where $F(x,t)$ has a locally square-integrable derivative in $x$ that satisfies a mild continuity condition in $t$ and…

In this paper we prove that the Benjamin-Ono equation, when considered on the torus, is an integrable (pseudo)differential equation in the strongest possible sense: it admits global Birkhoff coordinates on the space $L^2(\T)$. These are…

In [22], it was proved that as long as the integrand has certain properties, the corresponding It\^o integral can be written as a (parameterized) Lebesgue integral (or a Bochner integral). In this paper, we show that such a question can be…

We study an integro-differential equation which generalizes the periodic intermediate long wave (ILW) equation. The kernel of the singular integral involved is an elliptic function written as a second order difference of the Weierstrass…

A simple axiomatic characterization of the general (infinite dimensional, noncommutative) Ito algebra is given and a pseudo-Euclidean fundamental representation for such algebra is described. The notion of Ito B*-algebra, generalizing the…

We demonstrate that the necessary condition for $SO(N) \times SO(N)$ duality invariance manifests as a partial differential equation in two-dimensional scalar theories. This condition, expressed as a partial differential equation,…

In this note we investigate the behaviour of Brownian motion conditioned on a growth constraint of its local time which has been previously investigated by Berestycki and Benjamini. For a class of non-decreasing positive functions $f(t);…

The article is devoted to the expansion of iterated Ito stochastic integrals of second multiplicity based on expansion of the Brownian motion (standard Wiener process) using complete orthonormal systems of functions in the space $L_2([t,…

Let $X=\{X_n: n\in\mathbb{N}\}$ be a long memory linear process in which the coefficients are regularly varying and innovations are independent and identically distributed and belong to the domain of attraction of an $\alpha$-stable law…