Related papers: Stochastic Integrals on Predictable Sets of Interv…
A peculiar feature of It\^o's calculus is that it is an integral calculus that gives no explicit derivative with a systematic differentiation theory counterpart, as in elementary calculus. So, can we define a pathwise stochastic derivative…
The paper concerns itself with establishing large deviation principles for a sequence of stochastic integrals and stochastic differential equations driven by general semimartingales in infinite-dimensional settings. The class of…
In an M-type 2 Banach space, firstly we explore some properties of the set-valued stochastic integral associated with the stationary Poisson point process. By using the Hahn decomposition theorem and bounded linear functional, we obtain the…
The convergence of stochastic integrals is essential to stochastic analysis, especially in applications to mathematical finance, where they model the gains associated with a self-financing strategy. However, Fatou convergence of…
Stochastic integration \textit{wrt} Gaussian processes has raised strong interest in recent years, motivated in particular by its applications in Internet traffic modeling, biomedicine and finance. The aim of this work is to define and…
Let $(\mathcal{E},D(\mathcal{E}))$ be a quasi-regular semi-Dirichlet form and $(X_t)_{t\geq0}$ be the associated Markov process. For $u\in D(\mathcal{E})_{loc}$, denote $A_t^{[u]}:=\tilde{u}(X_{t})-\tilde{u}(X_{0})$ and…
Stochastic quantization in physics has been considered to provide a path integral representation of a probability distribution for Ito processes. It has been indicated that the stochastic quantization can involve a potential term, if the…
We use a path integral approach for solving the stochastic equations underlying the financial markets, and we show the equivalence between the path integral and the usual SDE and PDE methods. We analyze both the one-dimensional and the…
Let $\tilde{N}\_{t}$ be a standard compensated Poisson process on $[0,1]$. We prove a new characterization of anticipating integrals of the Skorohod type with respect to $\tilde{N}$, and use it to obtain several counterparts to well…
We consider some versions and generalizations of an approach to the expansion of iterated Ito stochastic integrals of arbitrary multiplicity $k$ $(k\in\mathbb{N})$ based on generalized multiple Fourier series. Expansions of iterated…
In the development of stochastic integration and the theory of semimartingales, Markov processes have been a constant source of inspiration. Despite this historical interweaving, it turned out that semimartingales should be considered the…
In the first part of the paper we study stochastic integrals of a nonrandom function with respect to a nonorthogonal Hilbert noise defined on a semiring of subsets of an arbitrary nonempty set. In the second part we apply this construction…
Several researchers have described two-part models with patient-specific stochastic processes for analysing longitudinal semicontinuous data. In theory, such models can offer greater flexibility than the standard two-part model with…
The `local time on curves' formula of Peskir provides a stochastic change of variables formula for a function whose derivatives may be discontinuous over a time-dependent curve, a setting which occurs often in applications in optimal…
We demonstrate that backward stochastic differential equations (BSDE) may be reformulated as ordinary functional differential equations on certain path spaces. In this framework, neither It\^{o}'s integrals nor martingale representation…
To model combinatorial decision problems involving uncertainty and probability, we introduce stochastic constraint programming. Stochastic constraint programs contain both decision variables (which we can set) and stochastic variables…
We consider the stochastic integrals of multivariate point processes and study their concentration phenomena. In particular, we obtain a Bernstein type of concentration inequality through Dol\'eans-Dade exponential formula and a uniform…
We develop the general integral transforms (GIT) method for pricing barrier options in the time-dependent Heston model (also with a time-dependent barrier) where the option price is represented in a semi-analytical form as a two-dimensional…
This essay explores the meaning of stochastic differential equations and stochastic integrals. It sets these subjects in a context of Riemann-Stieltjes integration. It is intended as a comment or supplement to \cite{MTRV}.
The purpose of these notes is to distribute, mostly without proofs, fundamental definitions and results concerning the theory of semimartingales and stochastic integration. The material serves as a foundational guide for those interested in…