Estimates of the Solutions of a System of Quasi-linear PDEs. A Probabilistic Scheme

By François Delarue. 2003

60 citations recorded by the source corpus.

Subfields: Applied Mathematics, Finance, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/045d3442215dcf16ac0a22963c8a327c2ffce115

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Citations in the corpus

A Forward-Backward Stochastic Algorithm For Quasi-Linear PDEs (2006, methodology): “Nevertheless, we are not able to apply the strategies used in [6, 7] to derive from the forward–backward writing local and global estimates of the discrete gradient of ū.”
CLASSICAL SOLUTIONS TO THE MASTER EQUATION FOR LARGE POPULATION EQUILIBRIA (2014, background): “bability, as a system with F0pX t,x,µ s ,rX t,ξ s sq as driver in the backward component and with b0pX t,x,µ s q ´ Z t,x,µ s ` p1{2qϕRpZ t,x,µ s q as drift in the forward component. In particular, by [11], there exists a constant Γ, independent of R, such that, whatever the length T is, any solution”
A class of globally solvable Markovian quadratic BSDE systems and applications (2016, methodology): “f the form |f(t,x,v,p)| ≤ ε|v|+P(|p|,|v|) (1+|p|)2 for some sufﬁciently small ε>0 and P(|p|,|v|) → 0 as |p| → ∞. When fhas at most linear growth in p, the same local estimate is established in [Del03] using a probabilistic techniques. (2) When v is Hölder continuous and there exists kn∈ Lq([0,T”
Control of McKean–Vlasov dynamics versus mean field games (2012, background): “Uniform continuity of the family (u)n≥1 on compact subsets follows from the smoothing effect of heat kernels, see [9].”
A Probabilistic Approach to Classical Solutions of the Master Equation for Large Population Equilibria (2014, background): “bability, as a system with F0pX t,x,µ s ,rX t,ξ s sq as driver in the backward component and with b0pX t,x,µ s q ´ Z t,x,µ s ` p1{2qϕRpZ t,x,µ s q as drift in the forward component. In particular, by [11], there exists a constant Γ, independent of R, such that, whatever the length T is, any solution”