We study a class of stochastic target games where one player tries to find a strategy such that the state process almost-surely reaches a given target, no matter which action is chosen by the opponent. Our main result is a geometric dynamic programming principle which allows us to characterize the value function as the viscosity solution of a non-linear partial differential equation. Because ab...

A new technique for continuous measurement of viscosityt and its application to studies of blood viscosity are described in this communication. For more than forty years viscosimetric studies of blood have been based on static, discrete determinations, such as that of Hess1 in which viscosity was considered to be inversely proportional to volume under given conditions of pressure in capillary t...

Microviscosity is of paramount importance in materials and bio-sciences. Fluorescence imaging using molecular rotors has emerged as a versatile tool to measure microviscosity, either using a fluorescence lifetime or a ratiometric signal of the rotor; however, only a limited number of blue-to-green-emitting fluorophores with both the lifetime and the ratiometric signal sensitivity to viscosity h...

We consider an optimal control problem of linear stochastic integro-differential equation with conic constraints on the phase variable and the control of singular-regular type. Our setting includes consumption-investment problems for models of financial markets in the presence of proportional transaction costs where that the prices are geometric Lévy processes and the investor is allowed to tak...

We study a stochastic game where one player tries to find a strategy such that the state process reaches a target of controlled-loss-type, no matter which action is chosen by the other player. We provide, in a general setup, a relaxed geometric dynamic programming for this problem and derive, for the case of a controlled SDE, the corresponding dynamic programming equation in the sense of viscos...

We study a problem of optimal investment/consumption over an infinite horizon in a market consisting of a liquid and an illiquid asset. The liquid asset is observed and can be traded continuously, while the illiquid one can only be traded and observed at discrete random times corresponding to the jumps of a Poisson process. The problem is a nonstandard mixed discrete/continuous optimal control ...

We obtain the uniqueness of lower semicontinuous (lsc for short) viscosity solutions of the transformed minimum time problem assuming that they converge to zero on a \reachable" part of the target in appropriate directions. We present a counterexample which shows that the uniqueness does not hold without this convergence assumption. It was shown by Soravia that the uniqueness of lsc viscosity s...

The main objective of this paper and the accompanying one [Viscosity solutions of fully nonlinear parabolic path dependent PDEs: Part II (2012) Preprint] is to provide a notion of viscosity solutions for fully nonlinear parabolic path-dependent PDEs. Our definition extends our previous work [Ann. Probab. (2014) 42 204–236], focused on the semilinear case, and is crucially based on the nonlinear...

S U M M A R Y Lateral viscosity variations (LVVs) in the mantle influence geodynamic processes and their surface expressions. With the observed long-wavelength geoid, free-air anomaly, gravity gradient in three directions and discrete, high-accuracy residual topography, we invert for depthand temperature-dependent and tectonically regionalized mantle viscosity with a mantle flow model. The inve...

Standard turbulence closures for large-eddy simulations of atmospheric flow based on finite-difference or finite-volume codes use eddy-viscosity models and hence ignore the contribution of the resolved subfilterscale stresses. These eddy-viscosity closures are unable to produce the expected logarithmic region near the surface in neutral boundary layer flows. Here, explicit filtering and reconst...