Related papers: Weak Dirichlet processes with jumps

Let $\xi_1$, $\xi_2,\ldots$ be i.i.d. random variables of zero mean and finite variance and $\eta_1$, $\eta_2,\ldots$ positive i.i.d. random variables whose distribution belongs to the domain of attraction of an $\alpha$-stable…

This article is devoted to the well-posedness of the stochastic compressible Navier Stokes equations. We establish the global existence of an appropriate class of weak solutions emanating from large inital data, set within a bounded domain.…

We consider a continuous-time financial market with an asset whose price is modeled by a linear stochastic differential equation with drift and volatility switching driven by a uniformly ergodic jump Markov process with a countable state…

Using changes of probability measure developed by \mbox{Grama} and Haeusler (Stochastic Process.\ Appl., 2000), we obtain two generalizations of the deviation inequalities of Lanzinger and Stadtm\"{u}ller (Stochastic Process.\ Appl., 2000)…

For a Gaussian process $X$ and smooth function $f$, we consider a Stratonovich integral of $f(X)$, defined as the weak limit, if it exists, of a sequence of Riemann sums. We give covariance conditions on $X$ such that the sequence converges…

We provide an It\^o's formula for $C^1$-functionals of flows of conditional marginal distributions of continuous semimartingales. This is based on the notion of weak Dirichlet process, and extends the $C^1$-It\^o's formula in Gozzi and…

Many time series are effectively generated by a combination of deterministic continuous flows along with discrete jumps sparked by stochastic events. However, we usually do not have the equation of motion describing the flows, or how they…

A novel approach is proposed to establish a sharp upper bound on the expected supremum of a separable martingale random field, serving as an alternative to classical universal chaining-based methods. The proposed approach begins by deriving…

This paper contributes to the study of relative martingales. Specifically, for a closed random set $H$, they are processes null on $H$ which decompose as $M=m+v$, where $m$ is a c\`adl\`ag uniformly integrable martingale and, $v$ is a…

For a semimartingale with jumps, we propose a new estimation method for integrated volatility, i.e., the quadratic variation of the continuous martingale part, based on the global jump filter proposed by Inatsugu and Yoshida [8]. To decide…

In this paper, we construct martingale suitable weak solutions for $3$-dimensional incompressible stochastic Navier-Stokes equations with generally non-linear noise. In deterministic setting, as widely known, ``suitable weak solutions'' are…

In this paper, we develop necessary and sufficient conditions for the validity of a martingale approximation for the partial sums of a stationary process in terms of the maximum of consecutive errors. Such an approximation is useful for…

We develop a non-anticipating calculus of variations for functionals on a space of laws of continuous semi-martingales, which extends the classical one. We extend Hamilton's least action principle and Noether's theorem to this generalized…

We consider a Markov process $X$ associated to a nonnecessarily symmetric Dirichlet form $\mathcal{E}$. We define a stochastic integral with respect to a class of additive functionals of zero quadratic variation and then we obtain an…

The paper is concerned with stochastic equations for the short rate process $R$ $$ dR(t)=F(R(t))dt+G(R(t-))dZ(t), $$ in the affine model of the bond prices. The equation is driven by a L\'evy martingale $Z$. It is shown that the discounted…

We develop a Malliavin calculus for nonlinear Hawkes processes in the sense of Carlen and Pardoux. This approach, based on perturbations of the jump times of the process, enables the construction of a local Dirichlet form. As an…

This paper contributes to the study of stochastic processes of the class $(\Sigma)$. First, we extend the notion of the above-mentioned class to c\`adl\`ag semi-martingales, whose finite variational part is considered c\`adl\`ag instead of…

We introduce Dirac processes, using Dirac delta functions, for short-rate-type pricing of financial derivatives. Dirac processes add spikes to the existing building blocks of diffusions and jumps. Dirac processes are Generalized Processes,…

The objective of this paper is to study the filtering problem for a system of partially observable processes $(X, Y)$, where $X$ is a non-Markovian pure-jump process representing the signal and $Y$ is a general jump-diffusion which provides…

We give sufficient criteria for the Dol\'eans-Dade exponential of a stochastic integral with respect to a counting process local martingale to be a true martingale. The criteria are adapted particularly to the case of counting processes and…