相关论文: The Donsker delta function and local time for McKe…

The study of the density evolution naturally arises in Mean Field Game theory for the estimation of the density of the large population dynamics. In this paper, we study the density evolution of McKean-Vlasov stochastic differential…

Using the balayage formula, we prove an inequality between the measures associated to local times of semimartingales. Our result extends the "comparison theorem of local times" of Ouknine $(1988)$, which is useful in the study of stochastic…

In this article, we consider fractional derivatives of local time for $d-$dimensional centered Gaussian processes satisfying certain strong local nondeterminism property. We first give a condition for existence of fractional derivatives of…

In this paper, we aim to study the asymptotic behaviour for a class of McKean-Vlasov stochastic partial differential equations with slow and fast time-scales. Using the variational approach and classical Khasminskii time discretization, we…

The Bismut formula is established for the intrinsic derivative of singular McKean-Vlasov SDEs, where the noise coefficient belongs to a local Sobolev space, and the drift contains a locally integrable time-space term as well as a…

In this paper, we present sufficient conditions and criteria to establish general large and moderate deviation principles for multivalued McKean-Vlasov stochastic differential equations (SDEs in short) by means of the weak convergence…

In this article we consider Bayesian estimation of static parameters for a class of partially observed McKean-Vlasov diffusion processes with discrete-time observations over a fixed time interval. This problem features several obstacles to…

In this paper, we consider the weak convergence of the Euler-Maruyama approximation for one dimensional stochastic differential equations involving the local times of the unknown process. We use a transformation in order to remove the local…

Under a Lipschitz condition on distribution dependent coefficients, the central limit theorem and the moderate deviation principle are obtained for solutions of McKean-Vlasov type stochastic differential equations, which extend from the…

In this paper, we address the full discretization of Friedrichs' systems with a two-field structure, such as Maxwell's equations or the acoustic wave equation in div-grad form, cf. [14]. We focus on a discontinuous Galerkin space…

The `local time on curves' formula of Peskir provides a stochastic change of variables formula for a function whose derivatives may be discontinuous over a time-dependent curve, a setting which occurs often in applications in optimal…

In this paper, we introduce the notion of efficiency (consistency) and examine some asymptotic properties of Markov chain Monte Carlo methods. We apply these results to the data augmentation (DA) procedure for independent and identically…

In this paper we consider a class of non-local in time telegraph equations. Recently, it has been proved that the fundamental solutions of such equations can be interpreted as the probability density function of a stochastic process. We…

The purpose of this paper is to investigate the existence of the Onsager-Machlup action functional for degenerate McKean-Vlasov stochastic differential equations. To this end, we first derive Onsager-Machlup action functional for degenerate…

Stochastic differential equations play an important role in various applications when modeling systems that have either random perturbations or chaotic dynamics at faster time scales. The time evolution of the probability distribution of a…

Three concepts of local times for deterministic c{\`a}dl{\`a}g paths are developed and the corresponding pathwise Tanaka--Meyer formulae are provided. For semimartingales, it is shown that their sample paths a.s. satisfy all three pathwise…

In this article we discuss the existence of local time for a class of Gaussian processes which appears as the solutions to some stochastic evolution equations. We show that on small intervals such processes are Gaussian integrators…

In this paper we give an explicit expression for the local time of the classical risk process and associate it with the density of an occupational measure. To do so, we approximate the local time by a suitable sequence of absolutely…

Many stochastic differential equations in various applications like coupled neuronal oscillators are driven by time-periodic forces. In this paper, we extend several data-driven computational tools from autonomous Fokker-Planck equation to…

We investigate the local times of a continuous-time Markov chain on an arbitrary discrete state space. For fixed finite range of the Markov chain, we derive an explicit formula for the joint density of all local times on the range, at any…