KRUSE Thomas

We consider the problem of optimally stopping a one-dimensional continuous-time Markov process with a stopping time satisfying an expectation constraint. We show that it is sufficient to consider only stopping times such that the law of the process at the stopping time is a weighted sum of 3 Dirac measures. The proof uses recent results on Skorokhod embeddings in order to reduce the stopping problem to a linear optimization problem over a convex set of probability measures.

We solve a class of BSDE with a power function f(y) = y^q , q > 1, driving its drift and with the singular terminal boundary condition given by the indicator function of the ball B(m,r) or of its complement, where B(m, r) is the ball in the path space of continuous paths on [0,T] of the underlying Brownian motion centered at the constant function m and radius r. The solution involves the derivation and solution of a related heat equation in which f serves as a reaction term and which is accompanied by singular and discontinuous Dirichlet boundary conditions. Although the solution of the heat equation is discontinuous at the corners of the domain the BSDE has continuous sample paths with the prescribed terminal value.

We solve a class of BSDE with a power function f(y) = y^q , q > 1, driving its drift and with the singular terminal boundary condition given by the indicator function of the ball B(m,r) or of its complement, where B(m, r) is the ball in the path space of continuous paths on [0,T] of the underlying Brownian motion centered at the constant function m and radius r. The solution involves the derivation and solution of a related heat equation in which f serves as a reaction term and which is accompanied by singular and discontinuous Dirichlet boundary conditions. Although the solution of the heat equation is discontinuous at the corners of the domain the BSDE has continuous sample paths with the prescribed terminal value.

We consider a variant of the basic problem of the calculus of variations, where the Lagrangian is convex and subject to randomness adapted to a Brownian filtration. We solve the problem by reducing it, via a limiting argument, to an unconstrained control problem that consists in finding an absolutely continuous process minimizing the expected sum of the Lagrangian and the deviation of the terminal state from a given target position. Using the Pontryagin maximum principle we characterize a solution of the unconstrained control problem in terms of a fully coupled forward-backward stochastic differential equation (FBSDE). We use the method of decoupling fields for proving that the FBSDE has a unique solution.

We consider the problem of optimally stopping a one-dimensional continuous-time Markov process with a stopping time satisfying an expectation constraint. We show that it is sufficient to consider only stopping times such that the law of the process at the stopping time is a weighted sum of 3 Dirac measures. The proof uses recent results on Skorokhod embeddings in order to reduce the stopping problem to a linear optimization problem over a convex set of probability measures.

In [8] we established existence and uniqueness of solutions of backward stochastic differential equations in L^p under a monotonicity condition on the generator and in a general filtration. There was a mistake in the case 1 < p < 2. Here we give a corrected proof. Moreover the quasi-left continuity condition on the filtration is removed.

Desulfitobacterium dehalogenans is able to grow by organohalide respiration using 3-chloro-4-hydroxyphenyl acetate (Cl-OHPA) as an electron acceptor. We used a combination of genome sequencing, biochemical analysis of redox active components, and shotgun proteomics to study elements of the organohalide respiratory electron transport chain. The genome of Desulfitobacterium dehalogenans JW/IU-DC1T consists of a single circular chromosome of 4,321,753 bp with a GC content of 44.97%. The genome contains 4,252 genes, including six rRNA operons and six predicted reductive dehalogenases. One of the reductive dehalogenases, CprA, is encoded by a well-characterized cprTKZEBACD gene cluster. Redox active components were identified in concentrated suspensions of cells grown on formate and Cl-OHPA or formate and fumarate, using electron paramagnetic resonance (EPR), visible spectroscopy, and high-performance liquid chromatography (HPLC) analysis of membrane extracts. In cell suspensions, these components were reduced upon addition of formate and oxidized after addition of Cl-OHPA, indicating involvement in organohalide respiration. Genome analysis revealed genes that likely encode the identified components of the electron transport chain from formate to fumarate or Cl-OHPA. Data presented here suggest that the first part of the electron transport chain from formate to fumarate or Cl-OHPA is shared. Electrons are channeled from an outward-facing formate dehydrogenase via menaquinones to a fumarate reductase located at the cytoplasmic face of the membrane. When Cl-OHPA is the terminal electron acceptor, electrons are transferred from menaquinones to outward-facing CprA, via an as-yet-unidentified membrane complex, and potentially an extracellular flavoprotein acting as an electron shuttle between the quinol dehydrogenase membrane complex and CprA.

We provide a new algorithm for approximating the law of a one-dimensional diffusion M solving a stochastic differential equation with possibly irregular coefficients. The algorithm is based on the construction of Markov chains whose laws can be embedded into the diffusion M with a sequence of stopping times. The algorithm does not require any regularity or growth assumption. in particular it applies to SDEs with coefficients that are nowhere continuous and that grow superlinearly. We show that if the diffusion coefficient is bounded and bounded away from zero, then our algorithm has a weak convergence rate of order 1/4. Finally, we illustrate the algorithm's performance with several examples.

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