Related papers: Uniqueness for the martingale problem associated w…
We describe the classes of functions $f=(f(x), x\in R)$, for which processes $f(W_t)-Ef(W_t)$ and $f(W_t)/Ef(W_t)$ are martingales. We apply these results to give a martingale characterization of general solutions of the quadratic and the…
For a real-valued one dimensional diffusive strict local martingale,, we provide a set of smooth functions in which the Cauchy problem has a unique classical solution under a local H\"older condition. Under the weaker Engelbert-Schmidt…
In this paper we present an algorithm to find the discrete Lagrangian for an autonomous recurrence relation of arbitrary even order $2k$ with $k>1$. The method is based on the existence of a set of differential operators called annihilation…
We consider specification and inference for the stochastic scale of discretely-observed pure-jump semimartingales with locally stable L\'{e}vy densities in the setting where both the time span of the data set increases, and the mesh of the…
A non-critical branching immigration superprocess with dependent spatial motion is constructed and characterized as the solution of a stochastic equation driven by a time-space white noise and an orthogonal martingale measure. A…
The main goal of this paper is to establish existence, regularity and uniqueness results for the solution of a Hamilton-Jacobi-Bellman (HJB) equation, whose operator is an elliptic integro-differential operator. The HJB equation studied in…
In this paper, we define an operator function as a series of operators corresponding to the Taylor series representing the function of the complex variable. In previous papers, we considered the case when a function has a decomposition in…
We consider a firm producing and selling $d$ commodities, and consisting from $n$ production and $m$ sales divisions. The firm manager tries to stimulate the best division performance by sequentially selecting internal commodity prices…
We consider second order linear differential operators possessing a term depending on the unknown function with a fixed argument and study the uniqueness of recovering the operators from the spectrum. We also obtain a constructive procedure…
This work shows how exponential concentration inequalities for additive functionals of stochastic processes over a finite time interval can be derived from concentration inequalities for martingales. The approach is entirely probabilistic…
A new integral with respect to an integer-valued random measure is introduced. In contrast to the finite variation integral ubiquitous in semimartingale theory (Jacod and Shiryaev, 2003, II.1.5), the new integral is closed under stochastic…
The objective of this article is to prove existence and weak uniqueness of a Walsh spider diffusion process, whose spinning measure and coefficients are allowed to depend on the local time spent at the junction vertex. The methodology is to…
In this paper, we consider a rather general linear evolution equation of fractional type, namely a diffusion type problem in which the diffusion operator is the $s$th power of a positive definite operator having a discrete spectrum in…
We present some analytical results for the stochastic sandpile model, studied earlier by Manna. In this model, the operators corresponding to particle addition at different sites commute. The eigenvalues of operators satisfy a system of…
In this paper we are interested on the well-posedness of Dirichlet problems associated to integro-differential elliptic operators of order $\alpha < 1$ in a bounded smooth domain $\Omega$ . The main difficulty arises because of losses of…
We report a new analytical method for exact solution of homogeneous linear ordinary differential equations with arbitrary order and variable coefficients. The method is based on the definition of jump transfer matrices and their extension…
We consider a stochastic perturbation of the $\alpha$-Navier-Stokes model. The stochastic perturbation is an additive space-time noise of trace class. Under a natural condition about the trace of operator $Q$ in front of the noise, we prove…
We consider a variable order differential operator on a graph with a cycle. We study the inverse spectral problem for this operator by the system of spectra. The main results of the paper are the uniqueness theorem and the constructive…
We consider a class of non-homogeneous Markov chains, that contains many natural examples. Next, using martingale methods, we establish some deviation and moment inequalities for separately Lipschitz functions of such a chain, under moment…
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…