相关论文: Stratonovich-type integral with respect to a gener…
The integral with respect to a multidimensional stochastic measure, for which we assume only $\sigma$-additivity in probability, is studied. The continuity and differentiability of its realizations are established.
A stochastic heat equation on $[0,T]\times{\mathbb{R}}$ driven by a general stochastic measure $d\mu(t)$ is investigated in this paper. For the integrator $\mu$, we assume the $\sigma$-additivity in probability only. The existence,…
We consider the stochastic transport equation where the randomness is given by the symmetric integral with respect to stochastic measure. For stochastic measure, we assume only $\sigma$-additivity in probability and continuity of paths. The…
This article presents a construction of the concept of stochastic integration in Riemannian manifolds from a purely functional-analytic point of view. We show that there are infinitely many such integrals, and that any two of them are…
We study one-dimensional stochastic integral equations with non-smooth dispersion coefficients, and with drift components that are not restricted to be absolutely continuous with respect to Lebesgue measure. In the spirit of Lamperti, Doss…
We examine the relation between a stochastic version of the rough path integral with the symmetric-Stratonovich integral in the sense of regularization. Under mild regularity conditions in the sense of Malliavin calculus, we establish…
We develop a general framework for pathwise stochastic integration that extends F\"ollmer's classical approach beyond gradient-type integrands and standard left-point Riemann sums and provides pathwise counterparts of It\^o, Stratonovich,…
Equation with the symmetric integral with respect to stochastic measure is considered. For the integrator, we assume only $\sigma$-additivity in probability and continuity of the paths. It is proved that the averaging principle holds for…
Let a sequence of iid. random variables $\xi_1,...,\xi_n$ be given on a measurable space $(X,\cal X)$ with distribution $\mu$ together with a function $f(x_1,...,x_k)$ on the product space $(X^k,{\cal X}^k)$. Let $\mu_n$ denote the…
Random functions $\mu(x)$, generated by values of stochastic measures are considered. The Besov regularity of the continuous paths of $\mu(x)$, $x\in[0,1]^d$ is proved. Fourier series expansion of $\mu(x)$, $x\in[0,2\pi]$ is obtained. These…
We develop a Fourier approach to rough path integration, based on the series decomposition of continuous functions in terms of Schauder functions. Our approach is rather elementary, the main ingredient being a simple commutator estimate,…
A new approach to stochastic integration is described, which is based on an a.s. pathwise approximation of the integrator by simple, symmetric random walks. Hopefully, this method is didactically more advantageous, more transparent, and…
A remarkable theorem of Besicovitch is that an integrable function $f$ on $\mathbb{R}^2$ is strongly differentiable if and only if its associated strong maximal function $M_S f$ is finite a.e. We provide an analogue of Besicovitch's result…
We to define a Path Integral in Lorentzian time by restricting the relevant domain of integration on $C([0,1],M)$ over a Riemannian configuration manifold $(M,g)$ and considering the dynamics of a particle evolving between to fixed…
This paper deals with stochastic integrals of form $\int_0^T f(X_u)d Y_u$ in a case where the function $f$ has discontinuities, and hence the process $f(X)$ is usually of unbounded $p$-variation for every $p\geq 1$. Consequently,…
The article is devoted to the expansions of iterated Stratonovich stochastic integrals of multiplicities 1 to 4 on the base of the combined approach of generalized multiple and iterated Fourier series. We consider two different parts of the…
The article is devoted to the expansions of iterated Stratonovich stochastic integrals on the basis of the method of generalized multiple Fourier series that converge in the sense of norm in Hilbert space $L_2([t, T]^k),$ $k\in\mathbb{N}.$…
Given $\{W^{(m)}(t), t \in [0,T]\}_{m \ge 1}$ a sequence of approximations to a standard Brownian motion $W$ in $[0,T]$ such that $W^{(m)}(t)$ converges almost surely to $W(t)$ we show that, under regular conditions on the approximations,…
In this article we study the existence of pathwise Stieltjes integrals of the form $\int f(X_t)\, dY_t$ for nonrandom, possibly discontinuous, evaluation functions $f$ and H\"older continuous random processes $X$ and $Y$. We discuss a…
The article is devoted to the construction of expansions of iterated Stratonovich stochastic integrals of fifth, sixth, seventh and eighth multiplicities based on the method of generalized multiple Fourier series converging in the sense of…