Weak Monotonicity Research Articles

Local existence and uniqueness of solutions to quadratic BSDEs with weak monotonicity and general growth generators

In this paper, we study quadratic backward stochastic differential equations (QBSDEs for short) with generators satisfying a weak monotonicity and a general growth condition with respect to the first variable. We provide the local existence and uniqueness of solutions to multi-dimensional QBSDEs. We use the convolution approach, the Picard iteration, the truncation and the Bihari inequality.

A Weak Monotonicity Based Muscle Fatigue Detection Algorithm for a Short-Duration Poor Posture Using sEMG Measurements.

Muscle fatigue is usually defined as a decrease in the ability to produce force. The surface electromyography (sEMG) signals have been widely used to provide information about muscle activities including detecting muscle fatigue by various data-driven techniques such as machine learning and statistical approaches. However, it is well-known that sEMGs are usually weak signals with a smaller amplitude and a lower signal-to-noise ratio, making it difficult to apply the traditional signal processing techniques. In particular, the existing methods cannot work well to detect muscle fatigue coming from static poses. This work exploits the concept of weak monotonicity, which has been observed in the process of fatigue, to robustly detect muscle fatigue in the presence of measurement noises and human variations. Such a population trend methodology has shown its potential in muscle fatigue detection as demonstrated by the experiment of a static pose.

A derivative-free three-term Hestenes–Stiefel type method for constrained nonlinear equations and image restoration

In this paper, a derivative-free Hestenes–Stielfel type method is proposed to solve large-scale nonlinear equations with convex constraints. The proposed method adopts the line search proposed by Ou and Li [J. Comput. Appl. Math. 56(1-2) (2018), pp. 195–216]. Unlike most existing methods, the global convergence of the proposed method is established under the assumption that the underlying mapping is Lipschitz continuous and satisfies a weaker monotonicity condition. Preliminary numerical experiments indicate that the proposed method is effective and promising. Furthermore, the proposed method is used to solve image restoration problem in compressive sensing.

Existence of solutions for a quasilinear elliptic system with variable exponent

We consider the following quasilinear elliptic system in a Sobolev space with variable exponent: [-text{div}(a(|Du|)Du)=f,] where $a$ is a $C^1$-function and $fin W^{-1,p'(x)}(Omega;R^m)$. We use the theory of Young measures and weak monotonicity conditions to obtain the existence of solutions.

Weak Solutions for Obstacle Problems with Weak Monotonicity

This paper is concerned with the existence of weak solutions for obstacle problems. By means of the Young measure theory and a theorem of Kinderlehrer and Stampacchia, we obtain the needed result.

Strong dissipativity of generalized time-fractional derivatives and quasi-linear (stochastic) partial differential equations

In this paper strong dissipativity of generalized time-fractional derivatives on Gelfand triples of properly in time weighted Lp-path spaces is proved. In particular, as special cases the classical Caputo derivative and other fractional derivatives appearing in applications are included. As a consequence one obtains the existence and uniqueness of solutions to evolution equations on Gelfand triples with generalized time-fractional derivatives. These equations are of typeddt(k⁎u)(t)+A(t,u(t))=f(t),0<t<T, with (in general nonlinear) operators A(t,⋅) satisfying general weak monotonicity conditions. Here k is a non-increasing locally Lebesgue-integrable nonnegative function on [0,∞) with lims→∞k(s)=0. Analogous results for the case, where f is replaced by a time-fractional additive noise, are obtained as well. Applications include generalized time-fractional quasi-linear (stochastic) partial differential equations. In particular, time-fractional (stochastic) porous medium and fast diffusion equations with ordinary or fractional Laplace operators and the time-fractional (stochastic) p-Laplace equation are covered.

Valuation monotonicity, fairness and stability in assignment problems

In two-sided assignment markets with transferable utility, we first introduce two weak monotonicity properties that are compatible with stability. We show that for a fixed population, the sellers-optimal (respectively the buyers-optimal) stable rules are the only stable rules that satisfy object-valuation antimonotonicity (respectively buyer-valuation monotonicity). Essential in these properties is that, after a change in valuations, monotonicity is required only for buyers that stay matched with the same seller. Using Owen's derived consistency, the two optimal rules are characterized among all allocation rules for two-sided assignment markets with a variable population, without explicitly requiring stability.Whereas these two monotonicity properties suggest an asymmetric treatment of the two sides of the market, valuation fairness axioms require a more balanced effect on the payoffs of buyers and sellers when the valuation of buyers for the objects owned by the sellers change. For assignment markets with a variable population, we introduce grand valuation fairness requiring that, if all valuations decrease by the same amount, as long as all optimal matchings still remain optimal, this leads to equal changes in the payoff of all agents. We show that the fair division rules are the only rules that satisfy this grand valuation fairness and a weak derived consistency property.

Directional Shift-Stable Functions

Recently, some new types of monotonicity—in particular, weak monotonicity and directional monotonicity of an n-ary real function—were introduced and successfully applied. Inspired by these generalizations of monotonicity, we introduce a new notion for n-ary functions acting on [0,1]n, namely, the directional shift stability. This new property extends the standard shift invariantness (difference scale invariantness), which can be seen as a particular directional shift stability. The newly proposed property can also be seen as a particular kind of local linearity. Several examples and a complete characterization for the case of n=2 of directionally shift-stable aggregation and pre-aggregation functions are also given.

Regularity and time behavior of the solutions to weak monotone parabolic equations

In this paper, we study the behavior in time of the solutions for a class of parabolic problems including the p-Laplacian equation and the heat equation. Either the case of singular or degenerate equations is considered. The initial datum u_0 is a summable function and a reaction term f is present in the problem. We prove that, despite the lack of regularity of u_0, immediate regularization of the solutions appears for data f sufficiently regular and we derive estimates that for zero data f become the known decay estimates for these kinds of problems. Besides, even if f is not regular, we show that it is possible to describe the behavior in time of a suitable class of solutions. Finally, we establish some uniqueness results for the solutions of these evolution problems.

Lp Solutions for Multidimensional BDSDEs with Locally Weak Monotonicity Coefficients

Lp Solutions for Multidimensional BDSDEs with Locally Weak Monotonicity Coefficients

On strongly quasilinear elliptic systems with weak monotonicity

Abstract In this paper, we prove existence results in the setting of Sobolev spaces for a strongly quasilinear elliptic system by means of Young measures and mild monotonicity assumptions.

Quasilinear Degenerated Elliptic Systems with Weighted in Divergence Form with Weak Monotonicity with General Data

We consider, for a bounded open domain Ω in Rn and a function u : Ω → Rm, the quasilinear elliptic system: (1). We generalize the system (QES)(f,g) in considering a right hand side depending on the jacobian matrix Du. Here, the star in (QES)(f,g) indicates that f may depend on Du. In the right hand side, v belongs to the dual space W-1,P’(Ω, ω*, Rm), , f and g satisfy some standard continuity and growth conditions. We prove existence of a regularity, growth and coercivity conditions for σ, but with only very mild monotonicity assumptions.

The Effects of Vietnam-Era Military Service on the Long-Term Health of Veterans: A Bounds Analysis

We analyze the short- and long-term effects of the U.S. Vietnam-era military service on veterans' health outcomes using a restricted version of the National Health Interview Survey 1974-2013 and employing the draft lotteries as an instrumental variable (IV). We start by assessing whether the draft lotteries, which have been used as an IV in prior literature, satisfy the exclusion restriction by placing bounds on its net or direct effect on the health outcomes of individuals who are non-veterans regardless of their draft eligibility (the never takers). Since we do not find evidence against the validity of the IV, we assume its validity in conducting inference on the health effects of military service for individuals who comply with the draft-lotteries assignment (the compliers), as well as for those who volunteer for enlistment (the always takers). The causal analysis for volunteers, who represent over 75% of veterans, is novel in this literature that typically focuses on the compliers. Since the effect for volunteers is not point-identified, we employ bounds that rely on a mild mean weak monotonicity assumption. We examine a large array of health outcomes and behaviors, including mortality, up to 40 years after the end of the Vietnam War. We do not find consistent evidence of detrimental health effects on compliers, in line with prior literature. For volunteers, however, we document that their estimated bounds show statistically significant detrimental health effects that appear 20 years after the end of the conflict. As a group, veterans experience similar statistically significant detrimental health effects from military service. These findings have implications for policies regarding compensation and health care of veterans after service.

An Example for 'Weak Monotone Comparative Statics'

An Example for 'Weak Monotone Comparative Statics'

Mean-field backward–forward stochastic differential equations and nonzero sum stochastic differential games

We study a general class of fully coupled backward–forward stochastic differential equations of mean-field type (MF-BFSDE). We derive existence and uniqueness results for such a system under weak monotonicity assumptions and without the non-degeneracy condition on the forward equation. This is achieved by suggesting an implicit approximation scheme that is shown to converge to the solution of the system of MF-BFSDE. We apply these results to derive an explicit form of open-loop Nash equilibrium strategies for nonzero sum mean-field linear-quadratic stochastic differential games with random coefficients. These strategies are valid for any time horizon of the game.

Well-Posedness and Exponential Estimates for the Solutions to Neutral Stochastic Functional Differential Equations with Infinite Delay

AbstractIn this work, neutral stochastic functional differential equations with infinite delay (NSFD-EwID) have been addressed. By using the Euler-Maruyama scheme and a localization argument, the existence and uniqueness of solutions to NSFDEwID at the state space Cr under the local weak monotone condition, the weak coercivity condition and the global condition on the neutral term have been investigated. In addition, the L2 and exponential estimates of NSFDEwID have been studied.

Existence of solutions for some quasilinear parabolic systems with weight and weak monotonicity general data

We prove the existence of weak solution u for the nonlinear parabolic systems: $$\begin{aligned} {(QPS){\omega }} \left\{ \begin{array}{rcl} \partial _{t} u -div\sigma (x,t,u,Du) &{} = &{} v(x,t) + f(x,t,u,Du) + divg(x,t,u)\; \text{ in } \;\; \Omega _{T}\\ u(x,t)&{} =&{} 0\;\; \text{ on } \;\;\partial \Omega \times (0,T)\\ u(x,0)&{} =&{}u_{0}(x)\;\; \text{ on } \;\;\Omega \end{array} \right. \end{aligned}$$ which is a Dirichlet Problem. In this system, v belongs to $$L^{p'}(0,T,W^{-1,p'}(\Omega ,\omega ^{*},\mathbb {R}^{m}))$$ and $$u_{0} \in L^{2}(\Omega ,\omega _{0}, \mathbb {R}^{m})$$ , f and g satisfy some standards continuity and growth conditions. We prove existence of a weak solution of different variants of this system under classical regularity for some $$p_{s}\in ]\frac{2n}{n+2}\; ;\;\infty [,$$ growth and coercivity for $$\sigma $$ but with only very mild monotonicity assumptions.

Backward Doubly SDEs with weak Monotonicity and General Growth Generators

We deal with backward doubly stochastic differential equations (BDSDEs) with a weak monotonicity and general growth generators and a square integrable terminal datum. We show the existence and uniqueness of solutions. As application, we establish the existenceand uniqueness of Sobolev solutions to some semilinear stochastic partial differential equations (SPDEs) with a general growth and a weak monotonicity generators. By probabilistic solution, we mean a solution which is representable throughout a BDSDEs.

Existence of solution for some quasilinear parabolic systems with weight and weak monotonicity

We prove the existence of weak solution u for the nonlinear parabolic systems: which is a Dirichlet Problem. In this system, v belongs to , f and g satisfy some standards continuity and growth conditions. We prove existence of a weak solution of different variants of this system under classical regularity for some growth and coercivity for σ but with only very mild monotonicity assumptions.

Influence in private-goods allocation

We reinterpret the ‘bossiness’ of a private-goods allocation rule (Satterthwaite and Sonnenschein, 1981) as the ability of an agent to ‘influence’ another’s welfare with no change to her own welfare. In applications where non-bossiness is not possible, we propose simple conditions on (1) which agents may have influence (acyclicity and preservation), and (2) the welfare consequences of influence (positivity and oppositeness). We apply these conditions to three well-known bossy rules: the ‘Vickrey rule’ in single-object auctions (Vickrey, 1961) (acyclic, positive), the ‘doctor-optimal stable rule’ in matching with contracts (Hatfield and Milgrom, 2005) (acyclic, positive, preserving) and ‘generalised absorbing top-trading cycles (GATTC) rules’ in housing markets with indifferences in preferences (Aziz and Keijzer, 2011) (acyclic, opposite, preserving). Under mild restrictions, we show how the nature of influence under a strategy-proof rule determines whether or not it satisfies weak group-strategy-proofness (requires acyclicity and either positivity or preservation), weak Maskin monotonicity (acyclicity and positivity) and Pareto-efficiency (acyclicity and oppositeness). In addition, we propose an influence-related generalisation of the efficiency-adjusted deferred acceptance mechanism in school choice (Kesten, 2010), and characterise influence for strategy-proof GATTC rules in housing markets.