相关论文: On the continuity of local times of Borel right Ma…

Continuity of local time for Brownian motion ranks among the most notable mathematical results in the theory of stochastic processes. This article addresses its implications from the point of view of applications. In particular an extension…

Let $Z = (Z_t)_{t \geq 0}$ be the Rosenblatt process with Hurst index $H \in (1/2, 1)$. We prove joint continuity for the local time of $Z$, and establish H\"older conditions for the local time. These results are then used to study the…

Several stochastic processes related to transient L\'evy processes with potential densities $u(x,y)=u(y-x)$, that need not be symmetric nor bounded on the diagonal, are defined and studied. They are real valued processes on a space of…

We study a Volterra Gaussian process of the form $X(t)=\int^t_0K(t,s)d{W(s)},$ where $W$ is a Wiener process and $K$ is a continuous kernel. In dimension one, we prove a law of the iterated logarithm, discuss the existence of local times…

We present sufficient conditions for the transience and the existence of local times of a Feller process, and the ultracontractivity of the associated Feller semigroup; these conditions are sharp for L\'{e}vy processes. The proof uses a…

This paper is devoted to the study of a certain type of martingale problems associated to general operators corresponding to processes which have finite lifetime. We analyse several properties and in particular the weak convergence of…

In this paper we study the local times of Brownian motion from the point of view of algorithmic randomness. We introduce the notion of effective local time and show that any path which is Martin-L\"of random with respect to the Wiener…

We obtain Sobolev regularity estimates for solutions of non-local parabolic equations with locally unbounded drift satisfying some minimal assumptions. These results yield Krylov bound for the corresponding Feller stable process as well as…

Let $X=\{X_{t},t\in R_{+}\}$ be a symmetric L\'{e}vy process with local time $\{L^{x}_{t} ; (x,t)\in R^{1}\times R^{1}_{+}\}$. When the L\'{e}vy exponent $\psi(\la)$ is regularly varying at zero with index $1<\beta\leq 2$, and satisfies…

Suppose that $(X_t)_{t \ge 0}$ is a one-dimensional Brownian motion with negative drift $-\mu$. It is possible to make sense of conditioning this process to be in the state $0$ at an independent exponential random time and if we kill the…

This article treats both discrete time and continuous time stopping problems for general Markov processes on the real line with general linear costs. Using an auxiliary function of maximum representation type, conditions are given to…

We present an exact expansion of the master equation for an open quantum system. The resulting equation is time local and enables us to calculate clearly defined higher order corrections to the Born-Markov approximation. In particular, we…

We show the complete proof of the Markov property of the strong solution to a multidimensional SDE whose coefficients involve local time on a hyperplane of the unknown process.

Permanental processes can be viewed as a generalisation of squared centered Gaussian processes. We develop in this paper two main subjects. The first one analyses the connections of these processes with the local times of general Markov…

We consider the existence and H\"{o}lder continuity conditions for the self-intersection local time of Rosenblatt process. Moreover, we study the cases of intersection local time and collision local time, respectively.

In this paper, we are concerned with centered Markov Additive Processes $\{(X_t,Y_t)\}_{t\in\T}$ where the driving Markov process $\{X_t\}_{t\in\T}$ has a finite state space. Under suitable conditions, we provide a local limit theorem for…

We investigate the connection between conditional local limit theorems and the local time of integer-valued stationary processes. We show that a conditional local limit theorem (at 0) implies the convergence of local times to Mittag-Leffler…

It is explained how a locally convex (lc) topology $\tau$ on a real vector space $V$ extends to a locally multiplicatively convex (lmc) topology $\overline{\tau}$ on the symmetric algebra $S(V)$. This allows the application of the results…

Following our previous work [68], this paper continues to investigate the evolution dynamics of local times of spectrally positive L\'evy processes with Gaussian components in the spatial direction. We prove that conditioned on the…

The theory of monotonicity and duality is developed for general one-dimensional Feller processes. Moreover it is shown that local monotonicity conditions (conditions on the L\'evy kernel) are sufficient to prove the well-posedness of the…