Related papers: Infinite dimensional polynomial processes
We consider the parabolic Anderson problem with random potentials having inverse-square singularities around the points of a standard Poisson point process in $\mathbb{R}^d$, $d \geq 3$. The potentials we consider are obtained via…
We derive P(M,t_m), the joint probability density of the maximum M and the time t_m at which this maximum is achieved for a class of constrained Brownian motions. In particular, we provide explicit results for excursions, meanders and…
We consider different types of processes obtained by composing Brownian motion $B(t)$, fractional Brownian motion $B_{H}(t)$ and Cauchy processes $% C(t)$ in different manners. We study also multidimensional iterated processes in…
We propose a method to compute an approximation of the moments of a discrete-time stochastic polynomial system. We use the Carleman linearization technique to transform this finite-dimensional polynomial system into an infinite-dimensional…
This paper studies value iteration for infinite horizon contracting Markov decision processes under convexity assumptions and when the state space is uncountable. The original value iteration is replaced with a more tractable form and the…
We consider the pricing problem related to payoffs that can have discontinuities of polynomial growth. The asset price dynamic is modeled within the Black and Scholes framework characterized by a stochastic volatility term driven by a…
In this paper, by using a Taylor development type formula, we show how it is possible to associate differential operators with stochastic differential equations driven by a fractional Brownian motion. As an application, we deduce that…
We consider one-dimensional diffusions, with polynomial drift and diffusion coefficients, so that in particular the motion can be space-inhomogeneous, interacting via one-sided reflections. The prototypical example is the well-known model…
In this paper, we present a general framework for solving stochastic functional differential equations in infinite dimensions in the sense of martingale solutions, which can be applied to a large class of SPDE with finite delays, e.g.…
We construct a planar diffusion process whose infinitesimal generator depends only on the order of the components of the process. Speaking informally and a bit imprecisely for the moment, imagine you run two Brownian-like particles on the…
We use variable transformation from the real line to finite or semi-infinite spaces where we expand the regular solution of the 1D time-independent Schrodinger equation in terms of square integrable bases. We also require that the basis…
Inspired by the recent work of Bertini and Posta, who introduced the boundary driven Brownian gas on $[0,1]$, we study boundary driven systems of independent particles in a general setting, including particles jumping on finite graphs and…
We study a stochastic control problem for a Volterra-type controlled forward equation with past dependence obtained via convolution with a deterministic kernel. To be able to apply dynamic programming to solve the problem, we lift it to…
The paper is devoted to quantization of polynomial momentum observables in the cotangent bundle of a smooth manifold. A quantization procedure is proposed allowing to quantize a wide class of functions which are polynomials of any order in…
Uniform large deviation principles for positive functionals of all equivalent types of infinite dimensional Brownian motions acting together with a Poisson random measure are established. The core of our approach is a variational…
We apply general moment identities for Poisson stochastic integrals with random integrands to the computation of the moments of Markovian growth-collapse processes. This extends existing formulas for mean and variance available in the…
We show the existence of superprocesses in a random medium with location dependent branching. Technically, we make use of a duality relation to establish the uniqueness of the martingale problem and to obtain the moment formulas.
A non-linear differential equation arising from a stochastic process known as branching Brownian motion is considered. We find an explicit solution and show the uniqueness of the solution under some boundedness conditions using…
We study multiple orthogonal polynomials exploiting their explicit determinantal representation in terms of moments. Our reasoning follows that applied to solve the Hermite-Pad\'{e} approximation and interpolation problems. We study also…
The $L^p$ maximal inequalities for martingales are one of the classical results in the theory of stochastic processes. Here we establish the sharp moderate maximal inequalities for one-dimensional diffusion processes, which include the…