Related papers: Joint distributions for stochastic functional diff…
We introduce a new class of numerical methods for solving McKean-Vlasov stochastic differential equations, which are relevant in the context of distribution-dependent or mean-field models, under super-linear growth conditions for both the…
We consider a stochastic functional differential equation with an arbitrary Lipschitz diffusion coefficient depending on the past. The drift part contains a term with superlinear growth and satisfying a dissipativity condition. We prove…
This paper explores the reconstruction of drift or diffusion coefficients of a scalar stochastic diffusion processes as it starts from an initial value and reaches, for the first time, a threshold value. We show that the distribution…
We investigate piecewise-linear stochastic models as with regards to the probability distribution of functionals of the stochastic processes, a question which occurs frequently in large deviation theory. The functionals that we are looking…
While the analytical solution for the marginal distribution of a stochastic chemical reaction network has been extensively studied, its joint distribution, i.e. the solution of a high-dimensional chemical master equation, has received much…
We present a detailed analysis of non-degenerate time-homogeneous It\^o-stochastic differential equations with low local regularity assumptions on the coefficients. In particular the drift coefficient may only satisfy a local integrability…
We study the convergence of the new family of mimetic finite difference schemes for linear diffusion problems recently proposed in [38]. In contrast to the conventional approach, the diffusion coefficient enters both the primary mimetic…
We introduce a lattice random walk discretisation scheme for stochastic differential equations (SDEs) that samples binary or ternary increments at each step, suppressing complex drift and diffusion computations to simple 1 or 2 bit random…
Reflected diffusions in polyhedral domains are commonly used as approximate models for stochastic processing networks in heavy traffic. Stationary distributions of such models give useful information on the steady state performance of the…
We present a generalization of Krylov-Rozovskii's result on the existence and uniqueness of solutions to monotone stochastic differential equations. As an application, the stochastic generalized porous media and fast diffusion equations are…
In this paper we discuss backward stochastic differential equations with Markov chain noise, having continuous drivers. We obtain the existence of a solution which is possibly not unique. Moreover, we show there is a minimal solution for…
We construct classes of stochastic differential equations with fluctuating friction forces that generate a dynamics correctly described by Tsallis statistics and nonextensive statistical mechanics. These systems generalize the way in which…
We present an approach to deep estimation of discrete conditional probability distributions. Such models have several applications, including generative modeling of audio, image, and video data. Our approach combines two main techniques:…
In this paper, we consider the problem of joint parameter estimation for drift and diffusion coefficients of a stochastic McKean-Vlasov equation and for the associated system of interacting particles. The analysis is provided in a general…
The density distributions and Soret coefficient in a nonequilibrium colloidal system with nonuniform temperature are studied by the overdamped Langevin equation for Brownian motion in an inhomogeneous strong friction medium. Based on the…
We design a numerical scheme for solving a Dynamic Programming equation with Malliavin weights arising from the time-discretization of backward stochastic differential equations with the integration by parts-representation of the…
The waiting time distribution (WTD) is a common tool for analysing discrete stochastic processes in classical and quantum systems. However, there are many physical examples where the dynamics is continuous and only approximately discrete,…
We close an unexpected gap in the literature of stochastic differential equations (SDEs) with drifts of super linear growth (and random coefficients), namely, we prove Malliavin and Parametric Differentiability of such SDEs. The former is…
It is shown that superpositions of path integrals with arbitrary Hamiltonians and different scaling parameters v ("variances") obey the Chapman-Kolmogorov relation for Markovian processes if and only if the corresponding smearing…
We derive an asymptotic expansion for the quadratic variation of a stochastic process satisfying a stochastic differential equation driven by a fractional Brownian motion, based on the theory of asymptotic expansion of Skorohod integrals…