LAUSR

Partial Differential Equations with Random Input Data: A Perturbation Approach

Sign Up to like & get
recommendations!
1 Published in 2018 at "Archives of Computational Methods in Engineering"

DOI: 10.1007/s11831-018-9275-2

Abstract: We study the numerical approximation of partial differential equations with random input data. Such problems arise when the uncertainty of the underlying system is taken into account using a probability setting. The main goal of… read more here.

Keywords: random input; partial differential; equations random; input data ... See more keywords

Backward doubly stochastic differential equations with random coefficients and quasilinear stochastic PDEs

Sign Up to like & get
recommendations!
0 Published in 2019 at "Journal of Mathematical Analysis and Applications"

DOI: 10.1016/j.jmaa.2018.10.038

Abstract: Abstract In this paper, by virtue of Malliavin calculus, we establish a relationship between backward doubly stochastic differential equations with random coefficients and quasilinear stochastic PDEs, and thus extend the well-known nonlinear stochastic Feynman–Kac formula… read more here.

Keywords: stochastic differential; doubly stochastic; random coefficients; backward doubly ... See more keywords

Convection–diffusion equations with random initial conditions

Sign Up to like & get
recommendations!
0 Published in 2019 at "Journal of Mathematical Analysis and Applications"

DOI: 10.1016/j.jmaa.2018.10.060

Abstract: Abstract We consider an evolution equation generalising the viscous Burgers equation supplemented by an initial condition which is a homogeneous random field. We develop a non-linear framework enabling us to show the existence and regularity… read more here.

Keywords: convection diffusion; equations random; initial conditions; diffusion equations ... See more keywords

Liouville’s equations for random systems

Sign Up to like & get
recommendations!
2 Published in 2021 at "Stochastic Analysis and Applications"

DOI: 10.1080/07362994.2021.1980015

Abstract: Given a random system, a Liouville’s equation is an exact partial differential equation that describes the evolution of the probability density function of the solution. In this article, we derive ... read more here.

Keywords: equations random; random systems; liouville equations;

Markov dependence in renewal equations and random sums with heavy tails

Sign Up to like & get
recommendations!
1 Published in 2017 at "Stochastic Models"

DOI: 10.1080/15326349.2017.1375860

Abstract: ABSTRACT The Markov renewal equation is considered in the subcritical case where the matrix of total masses of the Fij has spectral radius strictly less than one, and the asymptotics of the Zi(x) is found… read more here.

Keywords: random sums; equations random; dependence renewal; renewal ... See more keywords