The obstacle problem for quasilinear stochastic PDE’s

Abstract

We prove an existence and uniqueness result for the obstacle problem of quasilinear parabolic stochastic PDEs. The method is based on the probabilistic interpretation of the solution by using the backward doubly stochastic differential equation.

Reflected BSDEs and the obstacle problem for semilinear PDEs in divergence form

“…✷ Remark 4.7. In the particular case where L = ∂ ∂t + 1 2 ∆, f u ≡ 0, u is quasi-continuous and ϕ ≡ 0 results of Theorem 4.6 agree with those given in [24] (Theorem 2, Lemma 3), because the transition function p of the Wiener process is symmetric. For instance, integrating (4.8) with s = 0 with respect to m(dx) we get Theorem 3(v) in [24].…”

“…For instance, integrating (4.8) with s = 0 with respect to m(dx) we get Theorem 3(v) in [24]. Furthermore, taking expectation of (4.11) with s = 0, multiplying it by η ∈ L 2 (R d ) and then integrating with respect to m(dx) and using (4.8) we get Lemma 3 in [24]. We now recall the notion of soft measures (see [11]).…”

“…The above definition of a solution is a counterpart to the definition of a solution of the obstacle problem for elliptic equations (see, e.g., [2,16,21]). For parabolic equations such definition was considered earlier in few papers (see [24] and references therein) but only in case of more regular barriers, i.e. barriers for which (1.7) is satisfied.…”

The Effects of Governance Mechanisms on the Financial Information Quality

“…Forker (1992), for example, argued that that the separation of functions can increase the quality of control and reduce the probability of information retention of by leaders, which will substantially improve the quality of information disclosure. However, Hanifa and Cooke Finally, on a sample of 128 French companies belonging to the SBF250 index, Matoussi and Mahfoudh (2010) found that the separation between the functions of the chairman of the Board and those of the chief executive office compels the leader to engage in an "opportunistic" earnings management. This result is in line with the work carried out recently by Kantadu and Samaila (2015).…”

The obstacle problem for semilinear parabolic partial integro-differential equations

“…More recently, Matoussi and Stoica [37] studied the obstacle problem for parabolic quasilinear SPDEs and gave a probabilistic interpretation of the reflected measure ν in terms of the associated increasing process which is a component of solution of reflected BSDEs. Such measures are called regular measures or Revuz measures.…”