Related papers: Cylindrical Wiener processes
In this paper, we study integral functionals defined on spaces of functions with values on general (non-separable) Banach spaces. We introduce a new class of integrands and multifunctions for which we obtain measurable selection results.…
We work with very general Banach spaces of analytic functions in the disk or other domains which satisfy a minimum number of natural axioms. Among the preliminary results, we discuss some implications of the basic axioms and identify all…
We introduce Banach spaces of vector-valued random variables motivated from mathematical finance. So-called risk functionals are defined in a natural way on these Banach spaces and it is shown that these functionals are Lipschitz…
We introduce a variational theory for processes adapted to the multi-dimensional Brownian motion filtration. The theory provides a differential structure which describes the infinitesimal evolution of Wiener functionals at very small…
In this work, we present sufficient conditions for the existence of a stationary solution of an abstract stochastic Cauchy problem driven by an arbitrary cylindrical L\'evy process, and show that these conditions are also necessary if the…
The article is devoted to stochastic processes with values in finite- and infinite-dimensional vector spaces over infinite fields $\bf K$ of zero characteristics with non-trivial non-archimedean norms. For different types of stochastic…
The aim of this note is to provide some results for stochastic convolutions corresponding to stochastic Volterra equations in separable Hilbert space. We study convolution of the form $W^{\Psi}(t):=\int_0^t S(t-\tau)\Psi(\tau)dW(\tau)$,…
In a previous paper (PeCa24), the notion of Dirac structure in finite dimension was extended to the convenient setting. In particular, we introduce the notion of \emph{partial Dirac structure on a convenient manifold} and look for which all…
In this paper we present parallel theories on constructing Wiener algebras in the bicomplex setting. With the appropriate symmetry condition, the bicomplex matrix valued case can be seen as a complex valued case and, in this matrix valued…
Path integrals are a ubiquitous tool in theoretical physics. However, their use is sometimes hindered by the lack of control on various manipulations -- such as performing a change of the integration path -- one would like to carry out in…
The solution of a (stochastic) differential equation (SDE) can be locally approximated by a stochastic expansion, a linear combination of iterated integrals. Quantities of interest, like moments, can then be approximated with the expansion.…
In this paper, we introduce a definition of BV functions in a Gelfand triple which is an extension of the definition of BV functions in [2] by using Dirichlet form theory. By this definition, we can consider the stochastic reflection…
We show convexity of solutions to a class of convex variational problems in the Gauss and in the Wiener space. An important tool in the proof is a representation formula for integral functionals in this infinite dimensional setting, that…
We study the complexity of Banach space valued integration in the randomized setting. We are concerned with $r$-times continuously differentiable functions on the $d$-dimensional unit cube $Q$, with values in a Banach space $X$, and…
This paper presents a brief survey of the theory of stochastic integration in Banach spaces. Expositions of the stochastic integrals in martingale type 2 spaces and UMD spaces are presented, as well as some applications of the latter to…
Using the Euler--Maruyama technique, we show that a class of Wiener processes exist that are obtained by computing an arbitrary positive power of them. This can be accomplished with a proper set of definitions that makes meaningful the…
A Bochner integral formula is derived that represents a function in terms of weights and a parametrized family of functions. Comparison is made to pointwise formulations, norm inequalities relating pointwise and Bochner integrals are…
Existing concentration bounds for bounded vector-valued random variables include extensions of the scalar Hoeffding and Bernstein inequalities. While the latter is typically tighter, it requires knowing a bound on the variance of the random…
Stochastic integrals are defined with respect to a collection $P = (P_i; \, i \in I)$ of continuous semimartingales, imposing no assumptions on the index set $I$ and the subspace of $\mathbb{R}^I$ where $P$ takes values. The integrals are…
In this paper we collect several examples of convergence of functions of random processes to generalized functionals of those processes. We remark that the limit is always finitely absolutely continuous with respect to Wiener measure. We…