Related papers: Martingale Representation in Progressively Enlarge…
In this paper we give necessary and sufficient conditions for a cylindrical continuous local martingale to be the stochastic integral with respect to a cylindrical Brownian motion. In particular we consider the class of cylindrical…
Let $(X_t)_{t\ge0}$ be a continuous-time, time-homogeneous strong Markov process with possible jumps and let $\tau$ be its first hitting time of a Borel subset of the state space. Suppose $X$ is sampled at random times and suppose also that…
This paper is devoted to proving a general invariant representation theorem for generators of general time interval backward stochastic differential equations, where the generator $g$ has a quadratic growth in the unknown variable $z$ and…
We propose \textit{DeepMartingale}, a deep-learning framework for the dual formulation of discrete-monitoring optimal stopping problems under continuous-time models. Leveraging a martingale representation, our method implements a…
We discuss the Gamma Levy process, including path properties, the inverse process, integrability, and its spin-offs obtained by compounding, exponentiation, and other operations; further extendable to arbitrary sigma-finite continuous Borel…
This work is devoted to P\'olya-Young urns, a class of periodic P\'olya urns of importance in the analysis of Young tableaux. We provide several extension of the previous results of Banderier, Marchal and Wallner [Ann. Prob. (2020)] on…
Martingale representation theorem for set-valued martingales was proposed by M. Kisielewicz [J. Math. Anal. Appl. 2014]. We shall prove that the result holds only for very special case: the set-valued martingale degenerates to the…
In this paper, a study of random times on filtered probability spaces is undertaken. The main message is that, as long as distributional properties of optional processes up to the random time are involved, there is no loss of generality in…
We study frequency linear-time temporal logic (fLTL) which extends the linear-time temporal logic (LTL) with a path operator $G^p$ expressing that on a path, certain formula holds with at least a given frequency p, thus relaxing the…
The paper develops multiplicative compensation for complex-valued semimartingales and studies some of its consequences. It is shown that the stochastic exponential of any complex-valued semimartingale with independent increments becomes a…
Marginalization techniques are presented for the Bayesian filtering problem under the assumption of Gaussian priors and posteriors and a set of sequentially more constraining state space model assumptions. The techniques provide the…
Wright-Fisher diffusions describe the evolution of the type composition of an infinite haploid population with two types (say type $0$ and type $1$) subject to neutral reproductions, and possibly selection and mutations. In the present…
In this paper, we deal with a class of reflected backward stochastic differential equations associated to the subdifferential operator of a lower semi-continuous convex function driven by Teugels martingales associated with L\'{e}vy…
In this paper we derive the density $\varphi$ of the first time $T$ that a continuous martingale $M$ with non-random quadratic variation $<M>_\cdot:=\int_0^\cdot h^2(u)du$ hits a moving boundary $f$ which is twice continuously…
This paper considers discretization of the L\'evy process appearing in the Lamperti representation of a strictly positive self-similar Markov process. Limit theorems for the resulting approximation are established under some regularity…
We study the optional projection of a standard Brownian motion on the natural filtration of certain kinds of observation processes. The observation process, $Y$, is defined as a solution of a stochastic differential equation such that it…
We consider the problem of learning two families of time-evolving random measures from indirect observations. In the first model, the signal is a Fleming--Viot diffusion, which is reversible with respect to the law of a Dirichlet process,…
In this paper, we develop {finite-time horizon} causal filters using the nonanticipative rate distortion theory. We apply the {developed} theory to {design optimal filters for} time-varying multidimensional Gauss-Markov processes, subject…
We provide a general framework for dual representations of Laplace transforms of Markov processes. Such representations state that the Laplace transform of a finite-dimensional distribution of a Markov process can be expressed in terms of a…
Given a stochastic structure with a filtration $\mathbb{F}$, the class of all random times whose conditional distribution functions are differentiable with respect to some $\mathbb{F}$ adapted non decreasing processes is considered. The…