Related papers: Local Strict Comparison Theorem and Converse Compa…

In this note we study several topics related to the schema of local reflection $\mathsf{Rfn}(T)$ and its partial and relativized variants. Firstly, we introduce the principle of uniform reflection with $\Sigma_n$-definable parameters,…

We provide a necessary and sufficient condition for a rough control driving a differential equation to be reconstructable, to some order, from observing the resulting controlled evolution. Physical examples and applications in stochastic…

For the principal eigenvalue of discrete weighted $p$-Laplacian on the set of nonnegative integers, the convergence of an approximation procedure and the inverse iteration is proved. Meanwhile, in the proof of the convergence, the…

In this paper, we formulate a conjecture that describes the local theta correspondences in terms of the local Langland correspondences for rigid inner twists, which contain the correspondences for quaternionic dual pairs. Moreover, we…

We consider the method of alternating projections for finding a point in the intersection of two closed sets, possibly nonconvex. Assuming only the standard transversality condition (or a weaker version thereof), we prove local linear…

We establish transportation cost inequalities, with respect to the uniform and $L_2$-metric, on the path space of continuous functions, for laws of solutions of stochastic differential equations with reflections. We also consider the case…

In this paper we are concerned with a new type of backward equations with anticipation which we call neutral backward stochastic functional differential equations. We obtain the existence and uniqueness and prove a comparison theorem. As an…

We introduce a discretization/approximation scheme for reflected stochastic partial differential equations driven by space-time white noise through systems of reflecting stochastic differential equations. To establish the convergence of the…

Counterfactual examples are one of the most commonly-cited methods for explaining the predictions of machine learning models in key areas such as finance and medical diagnosis. Counterfactuals are often discussed under the assumption that…

Proof systems for the Relativized Propositional Calculus are defined and compared.

We give a counterexample to the PIA (precise inversion of adjunction) conjecture for minimal log discrepancies. We also give a counterexample to the LSC conjecture for families.

We prove a converse theorem for split even special orthogonal groups over finite fields. This is the only case left on converse theorems of split classical groups and the difficulty is the existence of the outer automorphism. In this paper,…

In this paper we establish a comparison theorem for stochastic differential delay equations with jumps. An example is constructed to demonstrate that the comparison theorem need not hold whenever the diffusion term contains a delay function…

We consider reflected backward stochastic different equations with optional barrier and so-called regulated trajectories, i.e trajectories with left and right finite limits. We prove existence and uniqueness results. We also show that the…

We prove existence and uniqueness of L^p solutions of reflected backward stochastic differential equations with p-integrable data and generators satisfying the monotonicity condition. We also show that the solution may be approximated by…

By using the Skorohod equation we derive an iteration procedure which allows us to solve a class of reflected backward stochastic differential equations with non-linear resistance induced by the reflected local time. In particular, we…

In this paper, we study a kind of constrained backward stochastic differential equations (BSDEs) such that the nonlinear expectation of the composition of a loss function and the solution remains above zero. The existence and uniqueness…

We study a random dynamical system such that one transformation is randomly selected from a family of transformations and then applied on each iteration. For such random dynamical systems, we consider estimates of absolutely continuous…

The (strong and weak) well-posedness is proved for singular SDEs depending on the distribution density point-wisely and globally, where the drift satisfies a local integrability condition in time-spatial variables, and is Lipschitz…

In this paper, we investigate the controlled system described by forward-backward stochastic differential equations with the control contained in drift, diffusion and generator of BSDE. A new verification theorem is derived within the…